#

J. A.
Abbott

# On the Factorization of Polynomials over Algebraic Fields

School of Mathematical Sciences, University of Bath
1989
September
Dean
Alvis
George
Lusztig

# Correction to the paper: The representations and generic degrees of the Hecke algebra of type H_4 [J. Reine Angew. Math. \bf 336 (1982), 201–212; MR0671329 (84a:20013)]

1994
449
217–218

Correction: ibid. \bf 449, 217–218 (1994)

AL82
0075-4102
MR1268587 (95a:20005)
20C15
Bhama Srinivasan
JRMAA8
Journal für die Reine und Angewandte Mathematik
Dean
Alvis
George
Lusztig

# The representations and generic degrees of the Hecke algebra of type H_4

1982
336
201–212

Correction: ibid. \bf 449, 217–218 (1994)

AL94
0075-4102
MR671329 (84a:20013)
20C15
Bhama Srinivasan
JRMAA8
Journal für die Reine und Angewandte Mathematik
Dean
Alvis

# The left cells of the Coxeter group of type H_4

1987
107
1
160–168
0021-8693
MR883878 (88d:20014)
20C15 (20C30 20H15)
Bhama Srinivasan
JALGA4
Journal of Algebra
D. G.
Arrell
S.
Manrai
M. F.
Worboys

# A procedure for obtaining simplified defining relations for a subgroup

Groups–St Andrews 1981 (St Andrews, 1981)
Cambridge Univ. Press
1982
Colin M.
Campbell
Edmund F.
Robertson
71
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155–159

    Cambridge

GrpsStAndrews81
0-521-28974-2
finitely presented groups; subgroup presentation, simplification; modified Todd Coxeter (mtc), tree decoding; algorithm description
MR679157 (84a:20041)
20F05 (20-04)
D. G.
Arrell
E. F.
Robertson

# A modified Todd-Coxeter algorithm

Computational group theory (Durham, 1982)
Academic Press
1984
Michael D.
Atkinson
27–32

    London

Durham1982
0-12-066270-1
finitely presented groups; subgroup presentation, simplification; modified Todd Coxeter (mtc), tree decoding; algorithm description
MR760644 (86g:20042)
20F05 (20-04)
I. D. Macdonald
E.
Artin

# Galoissche Theorie

Verlag Harri Deutsch
1973

    Zurich

Übersetzung nach der zweiten englischen Auflage besorgt von Viktor Ziegler, Mit einem Anhang von N. A. Milgram, Zweite, unveränderte Auflage, Deutsch-Taschenbücher, No. 21

MR0392905 (52 #13718)
12-02
86
Ulrich
Baum

# Existenz und effiziente Konstruktion schneller Fouriertransformationen überauflösbarer Gruppen

Rheinische Friedrich Wilhelm Universität Bonn
1991
Dissertation

    Bonn, Germany

Ulrich
Baum
Michael
Clausen

# Computing irreducible representations of supersolvable groups

1994
63
207
351–359
0025-5718
MR1226811 (94i:20029)
20C40 (20C15 68Q40)
Wolfgang Lempken
MCMPAF
Mathematics of Computation
László
Babai
Gene
Cooperman
Larry
Finkelstein
Ákos
Seress

# Nearly Linear Time Algorithms for Permutation Groups with a Small Base

Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC'91), Bonn 1991
1991
200–209
ACM Press
ISSAC91
M. J.
Beetham
C. M.
Campbell

# A note on the Todd-Coxeter coset enumeration algorithm

1976
20
1
73–79
0013-0915
finitely presented groups; subgroup presentation; modified Todd Coxeter (mtc); algorithm description
MR0399265 (53 #3116)
20F05
D. L. Johnson
Proceedings of the Edinburgh Mathematical Society. Series II
Mark
Benard

# Schur indices and splitting fields of the unitary reflection groups

1976
38
2
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0021-8693
MR0401901 (53 #5727)
20C30
Larry C. Grove
Journal of Algebra
C. T.
Benson
C. W.
Curtis

# On the degrees and rationality of certain characters of finite Chevalley groups

1972
165
251–273
0002-9947
MR0304473 (46 #3608)
20C30
A. Dress
Transactions of the American Mathematical Society
T. R.
Berger

# Characters and derived length in groups of odd order

1976
39
1
199–207
0021-8693
MR0396729 (53 #590)
20C15
I. M. Isaacs
Journal of Algebra
Hans Ulrich
Besche

# Die Berechnung von Charaktergraden und Charakteren endlicher auflösbarer Gruppen im Computeralgebrasystem GAP

Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule
1992
Diplomarbeit

    Aachen, Germany

Hans Ulrich
Besche
Bettina
Eick

# Construction of finite groups

1999
27
4
387–404
0747-7171
MR1681346 (2000c:20001)
20-04 (20D05 20D10)
Eamonn A. O'Brien
Journal of Symbolic Computation
Hans Ulrich
Besche
Bettina
Eick

# The groups of order at most 1000 except 512 and 768

1999
27
4
405–413
0747-7171
MR1681347 (2000c:20002)
20-04 (20D05 20D10)
Eamonn A. O'Brien
Journal of Symbolic Computation
Hans Ulrich
Besche
Bettina
Eick

# The groups of order q^n \cdot p

2001
29
4
1759–1772
0092-7872
MR1853124 (2002f:20028)
20D60
COALDM
Communications in Algebra
Hans Ulrich
Besche
Bettina
Eick
E. A.
O'Brien

# The groups of order at most 2000

2001
7
1–4 (electronic)
1079-6762
MR1826989
20D60
Electronic Research Announcements of the American Mathematical Society
Hans Ulrich
Besche
Bettina
Eick
E. A.
O'Brien

# A millennium project: constructing small groups

2002
12
5
623–644
0218-1967
MR1935567 (2003h:20042)
20D99
Robert M. Guralnick
International Journal of Algebra and Computation
F. Rudolf
Beyl
Ulrich
Felgner
Peter
Schmid

# On groups occurring as center factor groups

1979
61
1
161–177
0021-8693
MR554857 (81i:20034)
20E22
Richard E. Phillips
JALGA4
Journal of Algebra
Bettina
Eick
E. A.
O'Brien

# Enumerating p-groups

1999
67
2
191–205

Group theory

0263-6115
MR1717413 (2000h:20033)
20D15 (20J05)
Phạm Anh Minh
JAMADS
Australian Mathematical Society. Journal. Series A. Pure Mathematics and Statistics
Bettina
Eick
E. A.
O'Brien

# The groups of order 512

Algorithmic algebra and number theory (Heidelberg, 1997)
Springer
1999
B. H.
Matzat
G.-M.
Greuel
G.
Hiss
379–380

    Berlin

Proceedings of Abschlusstagung des DFG Schwerpunktes Algorithmische Algebra und Zahlentheorie in Heidelberg

MR1672078 (99m:20034)
20D15
M. F.
Newman
E. A.
O'Brien
M. R.
Vaughan-Lee

# Groups and nilpotent Lie rings whose order is the sixth power of a prime

2004
278
1
383–401
0021-8693
MR2068084 (2005c:20034)
20D15 (17B30)
Jeffrey M. Riedl
JALGA4
Journal of Algebra
E. A.
O'Brien
M. R.
Vaughan-Lee

# The groups with order p^7 for odd prime p

2005
292
1
243–258
0021-8693
MR2166803 (2006d:20038)
20D15 (17B30)
JALGA4
Journal of Algebra
Boris
Girnat

# Klassifikation der Gruppen bis zur Ordnung p^5

TU Braunschweig
2003
Staatsexamensarbeit

    Braunschweig, Germany

Heiko
Dietrich
Bettina
Eick

# On the groups of cube-free order

2005
292
1
122–137
0021-8693
MR2166799 (2006g:20001)
20-04 (20D06 20D10)
Eamonn A. O'Brien
JALGA4
Journal of Algebra
Thomas
Bischops

# Collectoren im Programmsystem GAP

Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule
1989
Diplomarbeit

    Aachen, Germany

Wieb
Bosma
John J.
Cannon

# Handbook of Cayley Functions

Department of Pure Mathematics, University of Sydney
1992

    Sydney, Australia

system design; Cayley;; manual
282 pp.
N.
Bourbaki

# Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines

Hermann
1968
Actualités Scientifiques et Industrielles, No. 1337

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MR0240238 (39 #1590)
22.50 (17.00)
G. B. Seligman
288 pp. (loose errata)
Richard P.
Brent
Graeme L.
Cohen

# A new lower bound for odd perfect numbers

1989
53
187
431–437, S7–S24
0025-5718
MR968150 (89m:11008)
11A25 (11Y05 11Y70)
Samuel S. Wagstaff, Jr.
MCMPAF
Mathematics of Computation
Thomas
Breuer

# Potenzabbildungen, Untergruppenfusionen, Tafel-Automorphismen

Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule
1991
Diplomarbeit

    Aachen, Germany

T.
Breuer
K.
Lux

# The multiplicity-free permutation characters of the sporadic simple groups and their automorphism groups

1996
24
7
2293–2316
0092-7872
MR1390375 (97c:20020)
20C34 (20D08)
Peter Fleischmann
COALDM
Communications in Algebra
Thomas
Breuer

# Integral bases for subfields of cyclotomic fields

1997
8
4
279–289
0938-1279
MR1464789 (99a:11120)
11R18
Wieb Bosma
AAECEW
Applicable Algebra in Engineering, Communication and Computing
Thomas
Breuer
Götz
Pfeiffer

# Finding possible permutation characters

1998
26
3
343–354
0747-7171
MR1633876 (99e:20005)
20B99 (20B40 20C15 20C40)
Cheryl E. Praeger
Journal of Symbolic Computation
Thomas
Breuer
Steve
Linton

# The GAP 4 Type System. Organizing Algebraic Algorithms

ISSAC '98: Proceedings of the 1998 international symposium on Symbolic and algebraic computation
1998
38–45

    New York, NY, USA

ACM Press

Chairman: Volker Weispfenning and Barry Trager

ISSAC98
1-58113-002-3
Rostock, Germany
ACM Order No.: 505980, ACM member price $25
Thomas
Breuer

# Computing possible class fusions from character tables

1999
27
6
2733–2748
0092-7872
MR1687309 (2000c:20015)
20C15
Jürgen Ritter
COALDM
Communications in Algebra
Thomas
Breuer
Simon P.
Norton

# Improvements to the Atlas

297–327
The Clarendon Press Oxford University Press
1995
11
London Mathematical Society Monographs. New Series

    New York

Appendix 2 by T. Breuer and S. Norton, Oxford Science Publications

JLPW95
0-19-851481-6
MR1367961 (96k:20016)
20C20 (20-00 20D06 20D08)
J. L. Alperin
E.
Brieskorn

# Die Fundamentalgruppe des Raumes der regulären Orbits einer endlichen komplexen Spiegelungsgruppe

1971
12
57–61
0020-9910
MR0293615 (45 #2692)
55A05
L. Neuwirth
Inventiones Mathematicae
Egbert
Brieskorn
Kyoji
Saito

# Artin-Gruppen und Coxeter-Gruppen

1972
17
245–271
0020-9910
MR0323910 (48 #2263)
20F05
D. E. Cohen
Inventiones Mathematicae
Michel
Broué
Gunter
Malle

# Zyklotomische Heckealgebren

Astérisque
1993
212
119–189

Représentations unipotentes génériques et blocs des groupes réductifs finis

Asterisque212
0303-1179
MR1235834 (94m:20095)
20G40 (20C20 20H15)
François Digne
Paris
Astérisque
Société Mathématique de France
Michel
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Michel

# Generic blocks of finite reductive groups

Astérisque
1993
212
7–92

Représentations unipotentes génériques et blocs des groupes réductifs finis

Asterisque212
0303-1179
MR1235832 (95d:20072)
20G05 (20C20)
Bhama Srinivasan
Paris
Astérisque
Société Mathématique de France
Michel
Broué
Gunter
Malle
Jean
Michel

# Représentations unipotentes génériques et blocs des groupes réductifs finis

Société Mathématique de France
1993

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Astérisque No. 212 (1993)

0303-1179
MR1235830 (94c:20078)
20G05
1–203
Alan
Baker

# A concise introduction to the theory of numbers

Cambridge University Press
1984

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0-521-24383-1; 0-521-28654-9
MR781734 (86f:11001)
11-01
Don Redmond
xiii+95
A. E.
Brouwer
A. M.
Cohen
A.
Neumaier

# Distance-regular graphs

Springer-Verlag
1989
18
Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)]

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3-540-50619-5
MR1002568 (90e:05001)
05-02 (05C75)
Joe Hemmeter
xviii+495
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Brown
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Joachim
Neubüser
Hans
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Hans
Zassenhaus

# Crystallographic groups of four-dimensional space

Wiley-Interscience [John Wiley & Sons]
1978

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Wiley Monographs in Crystallography

0-471-03095-3
MR0484179 (58 #4109)
82.20 (20F05)
Daniel B. Litvin
xiv+443
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Frank B.
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Charles F.
Miller III

# Some recognizable properties of solvable groups

1981
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MR635200 (82k:20061)
20F16 (03D40 20F10)
V. A. Romanʹkov
MAZEAX
Mathematische Zeitschrift
Gilbert
Baumslag
Frank B.
Cannonito
Charles F.
Miller III

# Computable algebra and group embeddings

1981
69
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186–212
0021-8693
MR613868 (82e:20042)
20F10 (03D40 03D45 16A53)
D. E. Cohen
JALGA4
Journal of Algebra
N.
Bourbaki

# Éléments de mathématique. Algèbre. Chapitres 1 à 3

Hermann
1970

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MR0274237 (43 #2)
00.00 (13.00)
P. Samuel
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D. L.
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E. F.
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# Some computations of nonabelian tensor products of groups

1987
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20F05 (20E22)
Stephen J. Pride
JALGA4
Journal of Algebra
Francis
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Dimitri
Leemans

# On the list of finite primitive permutation groups of degree \leq 50

1996
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MR1422147 (97g:20004)
20B15
Journal of Symbolic Computation
Gregory
Butler
John
McKay

# The transitive groups of degree up to eleven

1983
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20B05
Michael Klemm
COALDM
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Greg
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# The transitive groups of degree fourteen and fifteen

1993
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MR1271082 (95e:20006)
20B35 (20B40 68Q40)
Gerhard Hiss
Journal of Symbolic Computation
R. J.
Bradford

# On the computation of integral bases and defects of integrity

School of Mathematical Sciences, University of Bath
1989

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Bernard
Beauzamy
Vilmar
Trevisan
Paul S.
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# Polynomial factorization: sharp bounds, efficient algorithms

1993
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68Q40
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W.
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# Theory of groups of finite order

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1955

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20.0X
xxiv+512
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# Computing in permutation and matrix groups. II. Backtrack algorithm

1982
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0025-5718
permutation groups, matrix groups;; backtrack through stabilizer chain
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20-04 (20E25 20G40)
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MCMPAF
Mathematics of Computation
Gregory
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John
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# Computing in permutation and matrix groups. III. Sylow subgroups

1989
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20-04 (20D20)
J. D. Dixon
Journal of Symbolic Computation
Gregory
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# Effective computation with group homomorphisms

1985
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permutation groups; homomorphisms
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68Q40 (20-04 20B99)
Journal of Symbolic Computation
Harvey A.
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# An extension of coset enumeration

McGill University
1971
M. Sc. thesis

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finitely presented groups; subgroup presentation; modified Todd Coxeter (mtc); program description
John J.
Cannon

# Construction of defining relators for finite groups

1973
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105–129
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MR0318322 (47 #6869)
20F05
H. S. M. Coxeter
Discrete Mathematics
R. W.
Carter

# Conjugacy classes in the Weyl group

1972
25
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MR0318337 (47 #6884)
20H15 (17B20)
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Compositio Mathematica
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# Finite groups of Lie type

John Wiley & Sons Inc.
1985
Pure and Applied Mathematics (New York)

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Conjugacy classes and complex characters, A Wiley-Interscience Publication

0-471-90554-2
MR794307 (87d:20060)
20G40 (20-02 20C15)
David B. Surowski
xii+544
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# Finite groups of Lie type

John Wiley & Sons Ltd.
1993
Wiley Classics Library

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0-471-94109-3
MR1266626 (94k:20020)
20C33 (20-02 20G40)
xii+544
R. W.
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# Representation theory of the 0-Hecke algebra

1986
104
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MR865891 (88a:20014)
20C15 (16A65 20G05)
David Benson
JALGA4
Journal of Algebra
Roger W.
Carter

# Simple groups of Lie type

John Wiley & Sons, London-New York-Sydney
1972

Pure and Applied Mathematics, Vol. 28

MR0407163 (53 #10946)
20G15 (20D05 22E20)
Louis Solomon
viii+331
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# Simple groups of Lie type

John Wiley & Sons Inc.
1989
Wiley Classics Library

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0-471-50683-4
MR1013112 (90g:20001)
20-02 (20D05 20E32 20G15 20G40 22-02)
x+335
Frank
Celler

# Kohomologie und Normalisatoren in GAP

Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule
1992
Diplomarbeit

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F.
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J.
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C. R. B.
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# Some remarks on the computation of complements and normalizers in soluble groups

1990
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MR1085773 (91m:20026)
20D10 (20-04)
Michael C. Slattery
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Ruth
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# Artin groups of finite type are biautomatic

1992
292
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20F36 (20F10)
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MAANA
Mathematische Annalen
Michael
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# A direct proof of Minkwitz's extension theorem

1997
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20C15
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Applicable Algebra in Engineering, Communication and Computing
Henri
Cohen

# A course in computational algebraic number theory

Springer-Verlag
1993
138
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3-540-55640-0
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11Y40 (11Rxx 68Q40)
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xii+534
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# Calculating characters of p-groups

1990
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535–550

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20C40 (20C15 20D15)
Michael C. Slattery
Journal of Symbolic Computation
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# Computing modular and projective character degrees of soluble groups

1990
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551–570

Computational group theory, Part 1

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20C40 (20C15 20C20)
Michael C. Slattery
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R. T.
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S. P.
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R. A.
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R. A.
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# Atlas of finite groups

Oxford University Press
1985

    Eynsham

Maximal subgroups and ordinary characters for simple groups, With computational assistance from J. G. Thackray

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20D05 (20-02)
R. L. Griess
xxxiv+252
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John
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# On transitive permutation groups

LMS J. Comput. Math.
1998
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Larry
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# A random base change algorithm for permutation groups

1994
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MR1300351 (96a:68048)
68Q40 (20B07)
Journal of Symbolic Computation
David
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John
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# Ideals, varieties, and algorithms

Springer-Verlag
1997
Undergraduate Texts in Mathematics

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Second

An introduction to computational algebraic geometry and commutative algebra

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13P10 (13-01 14-01 14Qxx 68Q40)
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# Methods of representation theory. Vol. I

John Wiley & Sons Inc.
1981

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MR632548 (82i:20001)
20-02 (10C30 12A57 20Cxx)
J. L. Alperin
xxi+819
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Irving
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# Methods of representation theory. Vol. II

John Wiley & Sons Inc.
1987
Pure and Applied Mathematics (New York)

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With applications to finite groups and orders, A Wiley-Interscience Publication

0-471-88871-0
MR892316 (88f:20002)
20-02 (11Exx 18F25 19A31 19B28 19C99 20Cxx)
J. L. Alperin
xviii+951
Pierre
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# Les immeubles des groupes de tresses généralisés

1972
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0020-9910
MR0422673 (54 #10659)
32C40 (55A25)
Alan H. Durfee
Inventiones Mathematicae
Vinay V.
Deodhar

# A note on subgroups generated by reflections in Coxeter groups

1989
53
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20H15 (20F55)
François Digne
ACVMAL
Archiv der Mathematik
John D.
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# High speed computation of group characters

1967
10
446–450
0029-599X
MR0224726 (37 #325)
20.80 (65.00)
D. H. Lehmer
Numerische Mathematik
John D.
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Brian
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# The primitive permutation groups of degree less than 1000

1988
103
2
213–238
0305-0041
MR923674 (89b:20014)
20B10 (20B15 20B20)
Wolfgang Knapp
MPCPCO
Mathematical Proceedings of the Cambridge Philosophical Society
John D.
Dixon

# Constructing representations of finite groups

Groups and computation (New Brunswick, NJ, 1991)
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# A characterisation of solvable groups

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# Coxeter Version 1.0

Université de Lyon

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# Reflection subgroups of Coxeter systems

1990
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# The use of Knuth-Bendix methods to solve the word problem in automatic groups

1991
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MR1146506 (92m:68052)
68Q40 (03D40 20F10)
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Journal of Symbolic Computation
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# Special presentations for finite soluble groups and computing (pre-)Frattini subgroups

Groups and computation, II (New Brunswick, NJ, 1995)
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Werner
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# Computing maximal subgroups and Wyckoff positions of space groups

1997
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20H15 (82D25)
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# The solvable primitive permutation groups of degree at most 6560

LMS J. Comput. Math.
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Alexander
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# Computing the maximal subgroups of a permutation group I

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James W.
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Derek F.
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Michael S.
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# Word processing in groups

Jones and Bartlett Publishers
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MR1161694 (93i:20036)
20F10 (03D40 20-02 68Q70)
Richard M. Thomas
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Groups '93 Galway/St Andrews, Vol. 1 (Galway, 1993)
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MR1342790 (96d:20028)
20F05 (20F55)
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Volkmar
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Günter
Sandlöbes

# An interactive program for computing subgroups

Computational group theory (Durham, 1982)
Academic Press
1984
Michael D.
Atkinson
137–143

    London

Durham1982
0-12-066270-1
groups; subgroup lattice, table of marks; cyclic extensions; program description
MR760655 (85k:20003)
20-04 (20D10 68Q99)
Volkmar
Felsch
Joachim
Neubüser

# An algorithm for the computation of conjugacy classes and centralizers in p-groups

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Springer
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Edward W.
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EUROSAM '79, an International Symposium held in Marseille, June 1979

EUROSAM79
3-540-09519-5
MR575705 (82d:20003)
20-04
Colin M. Campbell
Paul
Fong

# Solvable groups and modular representation theory

1962
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20.80
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J. S.
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1982
10
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0172-1062
MR667230 (84a:20001)
20-04 (20C15)
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Bayreuther Mathematische Schriften

# GAP–Groups, Algorithms, and Programming, Version 4.4.9

The GAP Group
2006
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groups; *; gap; manual
http://www.gap-system.org

# GAP–Groups, Algorithms, and Programming, Version 4.4

The GAP Group
2004

http://www.gap-system.org

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groups; *; gap; manual
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# The braid group and other groups

1969
20
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MR0248801 (40 #2051)
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L. Neuwirth
The Quarterly Journal of Mathematics. Oxford. Second Series
Meinolf
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# On the character values of Iwahori-Hecke algebras of exceptional type

1994
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MR1243835 (94i:20073)
20F55 (20C15)
François Digne
PLMTAL
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M.
Geck

# Beiträge zur Darstellungstheorie von Iwahori-Hecke Algebren

Verlag der Augustinus Buchhandlung, Aachen
1995
11
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Meinolf
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Sungsoon
Kim

# Bases for the Bruhat-Chevalley order on all finite Coxeter groups

1997
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278–310
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20F55 (06A07)
Andrew Mathas
JALGA4
Journal of Algebra
Meinolf
Geck
Jean
Michel

# ``Good'' elements of finite Coxeter groups and representations of Iwahori-Hecke algebras

1997
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MR1425324 (97i:20050)
20F55 (20C20)
Stephen P. Humphries
PLMTAL
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Meinolf
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Götz
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# On the irreducible characters of Hecke algebras

1993
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20C15
Hiroshi Naruse
ADMTA4
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Meinolf
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Gerhard
Hiss
Frank
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Gunter
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1996
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20C40 (20C33)
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Stephan P.
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# Computational Approaches to the Theory of Finite Soluble Groups

Department of Pure Mathematics, University of Sydney
1987
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# Computing intersections and normalizers in soluble groups

1990
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20D10
Patrizia Longobardi
Journal of Symbolic Computation
Ronald L.
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Oren
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# Concrete mathematics

Addison-Wesley Publishing Company Advanced Book Program
1989

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MR1001562 (91f:00001)
00A05 (00-01 05-01 68-01 68Rxx)
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Arun
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1996
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# International tables for crystallography. Vol. A

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# International Tables for Crystallography, Vol. A

Kluwer, Dordrecht
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The Macmillan Co.
1964

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1988
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1969
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# A Reidemeister-Schreier program

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# Coset enumeration strategies

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# Integer matrix diagonalization

1997
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65F30 (65Y20)
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M. F.
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finitely presentend groups; Burnside groups; nilpotent quotient
MR586047 (82d:20002)
20-04 (20F50)
Colin M. Campbell
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P. E.
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# A Tietze transformation program

Computational group theory (Durham, 1982)
Academic Press
1984
Michael D.
Atkinson
69–73

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0-12-066270-1
finitely presented groups; simplification; Tietze
MR760651 (86b:20039)
20F05 (20-04)
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I. M.
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M.
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# On the Möbius function of a finite group

1989
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Gerhard
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Christoph
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Klaus
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Richard A.
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# Computational Modular Character Theory

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69–82

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MR1364180 (96m:20052)
20F10 (03D40 20-04 68Q40)
Sarah E. Rees
Derek F.
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C. R.
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E. A.
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Sarah
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# Computing matrix group decompositions with respect to a normal subgroup

1996
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20C40 (20B40)
Wolfgang Lempken
JALGA4
Journal of Algebra
Derek F.
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C. R.
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E. A.
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Sarah
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# Testing matrix groups for primitivity

1996
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795–817
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20C40 (20B40)
Wolfgang Lempken
JALGA4
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Derek F.
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W.
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# Perfect groups

The Clarendon Press Oxford University Press
1989
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With an appendix by W. Hanrath, Oxford Science Publications

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MR1025760 (91c:20029)
20D05 (20F05)
M. Ram Murty
xii+364
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Sarah
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# Testing modules for irreducibility

1994
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20C40
Herbert Pahlings
JAMADS
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George
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Colin
Ramsay

# Experiments in coset enumeration

Groups and computation, III (Columbus, OH, 1999)
de Gruyter
2001
William M.
Kantor
Ákos
Seress
8
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183–192

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3-11-016721-2
MR1829479 (2002e:20064)
20F05 (20-04)
Sarah E. Rees
George
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Colin
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# Proving a group trivial made easy: a case study in coset enumeration

2000
62
1
105–118
0004-9727
MR1775892 (2002j:20061)
20F05
E. F. Robertson
ALNBAB
Bulletin of the Australian Mathematical Society
J. M.
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1976

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L.M.S. Monographs, No. 7

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20MXX
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x+272
Alexander
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# Zur Berechnung von Charaktertafeln

Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule
1993
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Alexander
Hulpke

# Konstruktion transitiver Permutationsgruppen

Rheinisch Westfälische Technische Hochschule
1996
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Alexander
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# Computing normal subgroups

Proceedings of the 1998 International Symposium on Symbolic and Algebraic Computation (Rostock)
1998
194–198 (electronic)

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ACM

Chairman: Volker Weispfenning and Barry Trager

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1-58113-002-3
Rostock, Germany
MR1805183
20-04 (68W30)
ACM Order No.: 505980, ACM member price $25
Alexander
Hulpke

# Computing subgroups invariant under a set of automorphisms

1999
27
4
415–427
0747-7171
MR1681348 (2000a:20001)
20-04 (20D30)
D. F. Holt
Journal of Symbolic Computation
Alexander
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# Conjugacy classes in finite permutation groups via homomorphic images

2000
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MR1659847 (2001a:20006)
20B40
Alberto Delgado
MCMPAF
Mathematics of Computation
Alexander
Hulpke

# Representing subgroups of finitely presented groups by quotient subgroups

2001
10
3
369–381
1058-6458
MR1917425 (2003i:20049)
20F05 (20C34 20C40 68W30)
Dmitrii V. Pasechnik
Experimental Mathematics
Alexander
Hulpke

# Constructing transitive permutation groups

2005
39
1
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0747-7171
MR2168238 (2006e:20004)
20B10 (20B35)
J. Quistorff
Journal of Symbolic Computation
James E.
Humphreys

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Springer-Verlag
1972

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Graduate Texts in Mathematics, Vol. 9

MR0323842 (48 #2197)
17BXX
F. W. Lemire
xii+169
James E.
Humphreys

# Introduction to Lie algebras and representation theory

Springer-Verlag
1978
9
Graduate Texts in Mathematics

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Second printing, revised

0-387-90053-5
MR499562 (81b:17007)
17Bxx
I. P. Shestakov
xii+171
James E.
Humphreys

# Reflection groups and Coxeter groups

Cambridge University Press
1990
29
Cambridge Studies in Advanced Mathematics

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0-521-37510-X
MR1066460 (92h:20002)
20-02 (20F32 20F55 20G15 20H15)
Louis Solomon
xii+204
James E.
Humphreys

# Reflection groups and Coxeter groups

Cambridge University Press
1990
29
Cambridge Studies in Advanced Mathematics

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0-521-37510-X
MR1066460 (92h:20002)
20-02 (20F32 20F55 20G15 20H15)
Louis Solomon
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# Endliche Gruppen. I

Springer-Verlag
1967
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20.25
J. H. Walter
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Norman
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Springer-Verlag
1982
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3-540-10632-4
MR650245 (84i:20001a)
20-02 (20Dxx)
xiii+531
Bertram
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# Character theory of finite groups

Walter de Gruyter & Co.
1998
25
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3-11-015421-8
MR1645304 (99j:20011)
20C15 (20C05 20C10)
Gerhard Hiss
vi+618
I. Martin
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# Character theory of finite groups

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1976

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Pure and Applied Mathematics, No. 69

0-12-374550-0
MR0460423 (57 #417)
20-02
Stephen D. Smith
xii+303
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A. G.
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# Two-element generation of orthogonal groups over finite fields

1994
165
1
164–171
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MR1272584 (95b:20069)
20G40 (20F05)
Jia-Chen Ye
JALGA4
Journal of Algebra
Hiroyuki
Ishibashi
A. G.
Earnest

# Addendum: ``Two-element generation of orthogonal groups over finite fields'' [J. Algebra \bf 165 (1994), no. 1, 164–171; MR1272584 (95b:20069)]

1996
182
3
805
0021-8693
MR1398123 (97d:20061)
20G40 (20F05)
JALGA4
Journal of Algebra
Hiroyuki
Ishibashi
A. G.
Earnest

# Erratum: ``Two-element generation of orthogonal groups over finite fields'' [J. Algebra \bf 165 (1994), no. 1, 164–171; MR1272584 (95b:20069)]

1994
170
3
1035
0021-8693
MR1305274 (95h:20062)
20G40 (20F05)
JALGA4
Journal of Algebra
Christoph
Jansen
Klaus
Lux
Richard
Parker
Robert
Wilson

# An atlas of Brauer characters

The Clarendon Press Oxford University Press
1995
11
London Mathematical Society Monographs. New Series

    New York

Appendix 2 by T. Breuer and S. Norton, Oxford Science Publications

0-19-851481-6
MR1367961 (96k:20016)
20C20 (20-00 20D06 20D08)
J. L. Alperin
xviii+327
D. L.
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# Presentations of groups

Cambridge University Press
1997
15
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Second
0-521-58542-2
MR1472735 (98e:20001)
20-01 (20F05)
xii+216
Ansgar
Kaup

# Gitterbasen und Charaktere endlicher Gruppen

Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule
1992
Diplomarbeit

    Aachen, Germany

David
Kazhdan
George
Lusztig

# Representations of Coxeter groups and Hecke algebras

1979
53
2
165–184
0020-9910
MR560412 (81j:20066)
20H15 (17B35 20G05 22E47)
Vinay V. Deodhar
INVMBH
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Gregor
Kemper
Frank
Lübeck
Kay
Magaard

# Matrix generators for the Ree groups {}^2G_2(q)

2001
29
1
407–413
0092-7872
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20C33 (20D06)
COALDM
Communications in Algebra
Adalbert
Kerber

# Algebraic combinatorics via finite group actions

Bibliographisches Institut
1991

    Mannheim

3-411-14521-8
MR1115208 (92k:05130)
05E10 (20C30)
A. O. Morris
436
Wolfgang
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Richard
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Robert
Sandling
David N.
Teague

# Composition factors from the group ring and Artin's theorem on orders of simple groups

Proc. London Math. Soc. (3)
1990
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MR1023806 (91c:20030)
20D06 (20C05 20D60)
P. Fong
PLMTAL
Proceedings of the London Mathematical Society. Third Series
Peter
Kleidman
Martin
Liebeck

# The subgroup structure of the finite classical groups

Cambridge University Press
1990
129
London Mathematical Society Lecture Note Series

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0-521-35949-X
MR1057341 (91g:20001)
20-02 (20D06 20G40)
R. W. Carter
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A. U.
Klimyk

# Decomposition of the direct product of irreducible representations of semisimple Lie algebras into irreducible representations

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1966
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MR0206169 (34 #5991)
17.30 (22.60)
Renzo Cirelli
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# Decomposition of a direct product of irreducible representations of a semisimple Lie algebra into irreducible representations

American Mathematical Society Translations. Series 2
American Mathematical Society
1968
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Donald E.
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# The Art of Computer Programming, Volume 2: Seminumerical Algorithms

Addison-Wesley
1998
third
Donald E.
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# The art of computer programming. Vol. 2: Seminumerical algorithms

Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont
1969
MR0286318 (44 #3531)
68.00 (65.00)
M. Muller
xi+624
Reinhard
Laue

# Zur Konstruktion und Klassifikation endlicher auflösbarer Gruppen

Universität Bayreuth
1982
9
0172-1062
polycyclic groups;;; classification
MR651224 (84e:20018)
20D10 (20-02)
T. O. Hawkes
Bayreuther Mathematische Schriften
Bayreuth. Math. Schr.
PAGES: ii + 304, 1 correction sheet, Earlier version: Habilitationsschrift, RWTH Aachen, 1980
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MR 84e:20018 (T. O. Hawkes), Zbl 479.20010 (H. Heineken)
Reinhard
Laue
Joachim
Neubüser
Ulrich
Schoenwaelder

# Algorithms for finite soluble groups and the SOGOS system

Computational group theory (Durham, 1982)
1984
Michael D.
Atkinson
105–135

    London

Academic Press
Durham1982
0-12-066270-1
polycyclic groups;;; algorithm description
MR760654 (86h:20023)
20D10 (20-04 20D15 20F05 68Q40)
Gerhard Pazderski
MR 86h:20023 (Gerhard Pazderski), Zbl 547:20012 (E. Kommissartschik)
Philippe
LeChenadec

# Canonical forms in finitely presented algebras

Pitman Publishing Ltd.
1986
Research Notes in Theoretical Computer Science

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0-273-08721-5
MR840218 (88b:68117)
68Q50 (03B35 03D03 08B05 20F05 68Q40)
Friedrich Otto
xii+201
Charles R.
Leedham-Green
Leonard H.
Soicher

# Collection from the left and other strategies

1990
9
5-6
665–675

Computational group theory, Part 1

0747-7171
MR1075430 (92b:20021)
20D10 (68Q25)
M. Greendlinger
Journal of Symbolic Computation
A. K.
Lenstra
H. W.
Lenstra Jr.
L.
Lovász

# Factoring polynomials with rational coefficients

1982
261
4
515–534
LLL82
0025-5831
MR682664 (84a:12002)
12-04 (12A20 68C20 68C25)
Daniel Lazard
MAANA3
Mathematische Annalen
Jeffrey S.
Leon

# On an algorithm for finding a base and a strong generating set for a group given by generating permutations

1980
35
151
941–974
0025-5718
permutation groups; stabilizer chain, base and strong generating set of; Schreier Sims, Todd Coxeter (tc)
MR572868 (82i:20004)
20-04 (20F05)
Colin M. Campbell
MCMPAF
Mathematics of Computation
MR 82i:20004 (Colin M. Campbell), Zbl 444.20001 (J. Neubüser)
Jeffrey S.
Leon

# Permutation group algorithms based on partitions. I. Theory and algorithms

1991
12
4-5
533–583

Computational group theory, Part 2

0747-7171
MR1146516 (93c:68043)
68Q40 (20B40)
Jean Moulin Ollagnier
Journal of Symbolic Computation
Steve
Linton

# Vector Enumeration Programs, version 3

1993
E.
Lo

# A Polycyclic Quotient Algorithm

Rutgers University
1996
Frank
Lübeck

# Conway polynomials for finite fields

http://www.math.rwth-aachen.de:8001/~Frank.Luebeck/data/ConwayPol
2003
Eugene M.
Luks
Ferenc
Rákóczi
Charles R. B.
Wright

# Some algorithms for nilpotent permutation groups

1997
23
4
335–354
0747-7171
MR1445430 (97m:68113)
68Q40 (20B05)
Journal of Symbolic Computation
George
Lusztig

# On a theorem of Benson and Curtis

1981
71
2
490–498
0021-8693
MR630610 (83a:20053)
20G05 (14L30)
S. I. Gelʹfand
JALGA4
Journal of Algebra
George
Lusztig

# Characters of reductive groups over a finite field

Princeton University Press
1984
107
Annals of Mathematics Studies

    Princeton, NJ

0-691-08350-9; 0-691-08351-7
MR742472 (86j:20038)
20G05 (14L20 20C15)
Bhama Srinivasan
xxi+384
K.
Lux
H.
Pahlings

# Computational aspects of representation theory of finite groups

Representation theory of finite groups and finite-dimensional algebras (Bielefeld, 1991)
1991
G. O.
Michler
C. M.
Ringel
95
Progr. Math.
37–64

    Basel

Birkhäuser
MR91
3-7643-2604-2
MR1112157 (92g:20025)
20C40
Wolfgang Knapp
I. G.
Macdonald

# Numbers of conjugacy classes in some finite classical groups

1981
23
1
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0004-9727
MR615131 (82j:20092)
20G40
Naohisa Shimomura
ALNBAB
Bulletin of the Australian Mathematical Society
Meena
Mahajan
V.
Vinay

# Determinant: combinatorics, algorithms, and complexity

1997
Article 5, 26 pp. (electronic)
1073-0486
MR1484546 (98m:15016)
15A15 (05C50 68Q15 68Q22 68R05)
H.-J. Hoehnke
Chicago Journal of Theoretical Computer Science
Gunter
Malle

# Degrés relatifs des algèbres cyclotomiques associées aux groupes de réflexions complexes de dimension deux

Finite reductive groups (Luminy, 1994)
1997
Marc
Cabanes
141
Progr. Math.
311–332

    Boston, MA

Birkhäuser Boston

Related structures and representations

Luminy94
0-8176-3885-7
MR1429878 (98h:20019)
20C99 (20F55 20G40)
François Digne
Leonard
Soicher
John
McKay

# Computing Galois groups over the rationals

1985
20
3
273–281
0022-314X
MR797178 (87a:12002)
12-04 (11R32 11Y40)
Hale F. Trotter
JNUTA9
Journal of Number Theory
D. H.
McLain

# An algorithm for determining defining relations of a subgroup

1977
18
1
51–56
0017-0895
finitely presented groups; subgroup presentation; modified Todd Coxeter (mtc); algorithm description
MR0424950 (54 #12908)
20F05
N. S. Mendelsohn
Glasgow Mathematical Journal
MR 54 # 12908 (N. S. Mendelsohn), Zbl 348.20029 (Summary)
Matthias
Mecky
Joachim
Neubüser

# Some remarks on the computation of conjugacy classes of soluble groups

1989
40
2
281–292
0004-9727
MR1012835 (91i:20001)
20-04 (20D10)
ALNBAB
Bulletin of the Australian Mathematical Society
Thomas
Merkwitz

# Markentafeln endlicher Gruppen

Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule
1998
Diplomarbeit

    Aachen, Germany

Jürgen
Mnich

# Untergruppenverbände und auflösbare Gruppen in GAP

Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule
1992
Diplomarbeit

    Aachen, Germany

groups; subgroup lattice, table of marks; cyclic extensions; algorithm description
Peter L.
Montgomery

# Modular multiplication without trial division

1985
44
170
519–521
0025-5718
MR777282 (86e:11121)
11Y16
MCMPAF
Mathematics of Computation
Francis D.
Murnaghan

# The orthogonal and symplectic groups

Comm. Dublin Inst. Adv. Studies. Ser. A, no.
1958
13
146
MR0103933 (21 #2695)
20.00
J. S. Frame
John
McKay
Kiang Chuen
Young

# The nonabelian simple groups G, |G| < 10^{6}–minimal generating pairs

1979
33
146
812–814
0025-5718
MR521296 (80d:20018)
20D05 (20F05)
W. J. Wong
MCMPAF
Mathematics of Computation
B. D.
McKay

# nauty user's guide (version 1.5), Technical report TR-CS-90-02

Australian National University

    Computer Science Department, ANU

1990
Gabriele
Nebe

# Endliche rationale Matrixgruppen vom Grad 24

Rheinisch Westfälische Technische Hochschule
1995
Dissertation

    Aachen, Germany

Aachener Beiträge zur Mathematik
12
Gabriele
Nebe

# Finite subgroups of GL_n(Q) for 25 \leq n \leq 31

1996
24
7
2341–2397
0092-7872
MR1390378 (97e:20066)
20G15
Martin W. Liebeck
COALDM
Communications in Algebra
Joachim
Neubüser

# Die Untergruppenverbände der Gruppen der Ordnungen \leq 100 mit Ausnahme der Ordnungen 64 und 96

Universität Kiel
1967
Habilitationsschrift

    Kiel, Germany

PAGES: 370
Joachim
Neubüser

# An elementary introduction to coset table methods in computational group theory

Groups–St Andrews 1981 (St Andrews, 1981)
1982
Colin M.
Campbell
Edmund F.
Robertson
71
London Math. Soc. Lecture Note Ser.
1–45

    Cambridge

Cambridge Univ. Press
GrpsStAndrews81
0-521-28974-2
finitely presented groups; subgroup presentation, permutation representation, low index subgroups; Todd Coxeter (tc), modified Todd Coxeter (mtc); algorithm description, survey
MR679153 (84f:20004)
20-04 (20-02)
George Havas
MR 84f:20004 (George Havas), Zbl 489.20003 (G. Butler)
Jürgen
Neukirch

# Algebraische Zahlentheorie

Springer, Berlin, Heidelberg and New York
1992
Gabriele
Nebe
Wilhelm
Plesken

# Finite rational matrix groups of degree 16

74–144
AMS
1995
556

vol. 116

NPbook95
0065-9266
MR1265024 (95k:20081)
20H20 (11E57)
V. D. Mazurov
MAMCAU
Memoirs of the American Mathematical Society
Mem. Amer. Math. Soc.
G.
Nebe
W.
Plesken

# Finite rational matrix groups

AMS
1995
556
Mem. Amer. Math. Soc.

vol. 116

0065-9266
MR1265024 (95k:20081)
20H20 (11E57)
V. D. Mazurov
MAMCAU
Memoirs of the American Mathematical Society
Mem. Amer. Math. Soc.
viii+144
Joachim
Neubüser
Herbert
Pahlings
Wilhelm
Plesken

# CAS; design and use of a system for the handling of characters of finite groups

Computational group theory (Durham, 1982)
1984
Michael D.
Atkinson
195–247

    London

Academic Press
Durham1982
0-12-066270-1
ordinary representations; characters
MR760658 (86i:20004)
20-04 (20C15 20C30 68Q40)
D. Wales
MR 86i:20004 (D. Hales), Zbl 546.20001 (G. Butler)
Joachim
Neubüser
Wilhelm
Plesken
Hans
Wondratschek

# An emendatory discursion on defining crystal systems

1981
10
77–96
0340-6253
MR620802 (82i:20059)
20H15 (51F15 82A60)
Daniel B. Litvin
Proceedings of the Conference on Kristallographische Gruppen (Univ. Bielefeld, Bielefeld, 1979), Part II
MATCDV
Match
Zbl 551.20033 (Author)
M. F.
Newman

# Determination of groups of prime-power order

Group theory (Proc. Miniconf., Australian Nat. Univ., Canberra, 1975)
1977
R. A.
Bryce
J.
Cossey
Michael F.
Newman
573
Lecture Notes in Math.
73–84. Lecture Notes in Math., Vol. 573

    Berlin

Springer

Lecture Notes in Mathematics, Vol. 573

Canberra75
finitely presented groups, p-groups;; nilpotent quotient; application
MR0453862 (56 #12115)
20D15
Bruce W. King
MR 56 # 12115 (Bruce W. King), Zbl no ref
Michael F.
Newman

# Proving a group infinite

1990
54
3
209–211
0003-889X
MR1037607 (90j:20068)
20F05
D. L. Johnson
ACVMAL
Archiv der Mathematik
Michael F.
Newman
Eamonn A.
O'Brien

# A CAYLEY library for the groups of order dividing 128

Group theory (Singapore, 1987)
1989
Kai Nah
Cheng
Yu Kiang
Leong
437–442

    Berlin

de Gruyter
Singapore87
3-11-011366-X
MR981861 (90b:20002)
20-04 (20D15)
J. McKay
Felix
Noeske

# Zur Darstellungstheorie der Schurschen Erweiterungen symmetrischer Gruppen

Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule
2002
Diplomarbeit
Eamonn A.
O'Brien

# The p-group generation algorithm

1990
9
5-6
677–698

Computational group theory, Part 1

0747-7171
MR1075431 (91j:20050)
20D15
È. M. Palʹchik
Journal of Symbolic Computation
Eamonn A.
O'Brien

# The groups of order 256

1991
143
1
219–235
0021-8693
MR1128656 (93e:20029)
20D15 (20-04)
JALGA4
Journal of Algebra
Eamonn A.
O'Brien

# Isomorphism testing for p-groups

1994
17
2
131, 133–147
0747-7171
MR1283739 (95f:20040b)
20D15 (20D45 20F28)
Richard Davitt
Journal of Symbolic Computation
Eamonn A.
O'Brien

# Computing automorphism groups of p-groups

Computational algebra and number theory (Sydney, 1992)
1995
Wieb
Bosma
Alf
van der Poorten
325
83–90

    Dordrecht

Kluwer Acad. Publ.
MR1344923 (96g:20024)
20D15 (20D45)
Wolfgang Lempken
Michael F.
Newman
Eamonn A.
O'Brien

# Application of computers to questions like those of Burnside. II

1996
6
5
593–605
0218-1967
MR1419133 (97k:20002)
20-04 (20D15 20F05)
Colin M. Campbell
International Journal of Algebra and Computation
Thomas
Ostermann

# Charaktertafeln von Sylownormalisatoren sporadischer einfacher Gruppen

Universität Essen
1986

    Essen

MR872094 (88g:20002)
20-04 (20C20 20D08)
M. F. Newman
x+187
Universität Essen Fachbereich Mathematik
Vorlesungen aus dem Fachbereich Mathematik der Universität GH Essen [Lecture Notes in Mathematics at the University of Essen]
14
Herbert
Pahlings

# On the Möbius function of a finite group

1993
60
1
7–14
0003-889X
MR1193087 (94c:20039)
20D30
David Gluck
ACVMAL
Archiv der Mathematik
Richard A.
Parker

# The computer calculation of modular characters (the meat-axe)

Computational group theory (Durham, 1982)
1984
Michael D.
Atkinson
267–274

    London

Academic Press
Durham1982
0-12-066270-1
MR760660 (85k:20041)
20C20 (20-04)
Leo J. Alex
G.
Pfeiffer

# Von Permutationscharakteren und Markentafeln

Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule
1991
Diplomarbeit

    Aachen, Germany

Götz
Pfeiffer

# Character tables of Weyl groups in GAP

1994
47
165–222
0172-1062
MR1285208 (95d:20027)
20C40 (20C15 20D06 20F40)
Stephen A. Linton
Bayreuther Mathematische Schriften
Götz
Pfeiffer

# Young characters on Coxeter basis elements of Iwahori-Hecke algebras and a Murnaghan-Nakayama formula

1994
168
2
525–535
0021-8693
MR1292779 (95g:20012)
20C30 (20C15 20F55)
Arun Ram
JALGA4
Journal of Algebra
Götz
Pfeiffer

# Character values of Iwahori-Hecke algebras of type B

Finite reductive groups (Luminy, 1994)
1997
Marc
Cabanes
141
Progr. Math.
333–360

    Boston, MA

Birkhäuser Boston

Related structures and representations

Luminy94
0-8176-3885-7
MR1429879 (98a:20008)
20C15 (20F55)
Robert Bédard
Götz
Pfeiffer

# The subgroups of M_{24}, or how to compute the table of marks of a finite group

1997
6
3
247–270
1058-6458
MR1481593 (98h:20032)
20D30 (20D08)
A. S. Kondratʹev
Experimental Mathematics
Günter
Pilz

# Near-rings

North-Holland Publishing Co.
1983
23
North-Holland Mathematics Studies

    Amsterdam

Second

The theory and its applications

0-7204-0566-1
MR721171 (85h:16046)
16A76 (16-02)
J. R. Clay
xv+470
Wilhelm
Plesken

# Finite unimodular groups of prime degree and circulants

1985
97
1
286–312
0021-8693
MR812182 (87c:20020)
20C10 (20G40)
Wolfgang Knapp
JALGA4
Journal of Algebra
Wilhelm
Plesken

# Solving XX^{\rm tr} = A over the integers

1995
226/228
331--344
0024-3795
MR1344572 (96h:15016)
15A24
M. C. Chaki
LAAPAW
Linear Algebra and its Applications
Wilhelm
Plesken
Gabriele
Nebe

# Finite rational matrix groups

1–73
AMS
1995
556

vol. 116

NPbook95
0065-9266
MR1265024 (95k:20081)
20H20 (11E57)
V. D. Mazurov
MAMCAU
Memoirs of the American Mathematical Society
Mem. Amer. Math. Soc.
G.
Nebe
W.
Plesken

# Finite rational matrix groups

1995
116
556
viii+144
0065-9266
MR1265024 (95k:20081)
20H20 (11E57)
V. D. Mazurov
MAMCAU
Memoirs of the American Mathematical Society
Wilhelm
Plesken
Michael
Pohst

# On maximal finite irreducible Subgroups of GL(n,Z). I. The five and seven dimensional cases, II. The six dimensional case

1977
31
536–576
MR 56 # 3137a, 3137b (Wolfgang Knapp), Zbl 359.20006, 359.20007 (authors)
Wilhelm
Plesken
Michael
Pohst

# On maximal finite irreducible subgroups of GL(n, Z). I. The five and seven dimensional cases

1977
31
138
536–551
0025-5718
MR0444789 (56 #3137a)
20G05
Wolfgang Knapp
Mathematics of Computation
Wilhelm
Plesken
Michael
Pohst

# On maximal finite irreducible subgroups of GL(n, Z). II. The six dimensional case

1977
31
138
552–573
0025-5718
MR0444790 (56 #3137b)
20G05
Wolfgang Knapp
Mathematics of Computation
Wilhelm
Plesken
Michael
Pohst

# On maximal finite irreducible Subgroups of GL(n,Z). III. The nine dimensional case, IV. Remarks on even dimensions with application to n = 8, V. The eight dimensional case and a complete description of dimensions less than ten

1980
34
245–301
MR 81b:20012a, 81b:20012b, 81b:20012c (Wolfgang Knapp), Zbl 431.20039, 431.20040, 431.20041 (authors)
Wilhelm
Plesken
Michael
Pohst

# On maximal finite irreducible subgroups of GL(n, Z). III. The nine-dimensional case

1980
34
149
245–258
0025-5718
MR551303 (81b:20012a)
20C10
Wolfgang Knapp
MCMPAF
Mathematics of Computation
Wilhelm
Plesken
Michael
Pohst

# On maximal finite irreducible subgroups of GL(n, Z). IV. Remarks on even dimensions with applications to n = 8

1980
34
149
259–275
0025-5718
MR551304 (81b:20012b)
20C10
Wolfgang Knapp
MCMPAF
Mathematics of Computation
Wilhelm
Plesken
Michael
Pohst

# On maximal finite irreducible subgroups of GL(n, Z). V. The eight-dimensional case and a complete description of dimensions less than ten

1980
34
149
277–301, loose microfiche suppl
0025-5718
MR551305 (81b:20012c)
20C10
Wolfgang Knapp
MCMPAF
Mathematics of Computation
M.
Pohst

# A modification of the LLL reduction algorithm

1987
4
1
123–127
0747-7171
MR908420 (89c:11183)
11Y16 (11H06 11R27 11Y05 68Q20)
Hans G. Kopetzky
Journal of Symbolic Computation
Arun
Ram

# A Frobenius formula for the characters of the Hecke algebras

1991
106
3
461–488
0020-9910
MR1134480 (93c:20029)
20C30 (05E05 16W30 17B37)
Jie Du
INVMBH
Inventiones Mathematicae
Colin
Ramsay

# ACE for Amateurs

Centre for Discrete Mathematics and Computing, The University of Queensland
1999

Draft

C.
Ramsay

# ACE User Manual

    Department   of   Computer   Science   &   Electrical
                          Engineering   and   Department   of  Mathematics,  The
      University of Queensland, QLD 4072, Australia

1999

Draft

Centre for Discrete Mathematics and Computing
Michael
Ringe

# The C MeatAxe, Release 1.5

Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule

    Aachen, Germany

1993
Michael
Ringe

# The C MeatAxe, Release 2.3

Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule

    Aachen, Germany

1998
Edmund F.
Robertson

# Tietze transformations with weighted substring search

1988
6
1
59–64
0747-7171
finitely presented groups; simplification; Tietze transformations
MR961370 (89h:68076)
68Q40 (20F05)
Journal of Symbolic Computation
Colva M.
Roney-Dougal
William R.
Unger

# The affine primitive permutation groups of degree less than 1000

2003
35
4
421–439
0747-7171
MR1976576 (2004e:20002)
20B15
Xianhua Li
Journal of Symbolic Computation
Colva M.
Roney-Dougal

# The primitive permutation groups of degree less than 2500

2005
292
1
154–183
0021-8693
MR2166801 (2006e:20005)
20B15
Michael Giudici
JALGA4
Journal of Algebra
Gordon F.
Royle

# The transitive groups of degree twelve

1987
4
2
255–268
0747-7171
MR922391 (89b:20010)
20B05
Martin W. Liebeck
Journal of Symbolic Computation
L. J.
Rylands
D. E.
Taylor

# Matrix generators for the orthogonal groups

1998
25
3
351–360
0747-7171
MR1615330 (99d:20078)
20G40
A. G. Earnest
Journal of Symbolic Computation
L. L.
Scott

# Modular permutation representations

1973
175
101–121
0002-9947
MR0310051 (46 #9154)
20C20
H. K. Farahat
Transactions of the American Mathematical Society
Gerhard J. A.
Schneider

# Dixon's character table algorithm revisited

1990
9
5-6
601–606

Computational group theory, Part 1

0747-7171
MR1075426 (91j:20036)
20C40 (20-04 20C15 68Q40)
Jamshid Moori
Journal of Symbolic Computation
Michael
Scherner

# Erweiterung einer Arithmetik von Kreisteilungskörpern auf deren Teilkörper und deren Implementation in GAP

Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule
1992
Diplomarbeit

    Aachen, Germany

Ute
Schiffer

# Cliffordmatrizen

Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule
1994
Diplomarbeit

    Aachen, Germany

Ákos
Seress

# Nearly linear time algorithms for permutation groups: an interplay between theory and practice

1998
52
1-3
183–207

Algebra and combinatorics: interactions and applications (Königstein, 1994)

0167-8019
MR1649697 (2000e:20008)
20B40 (20-04 68W30)
Miguel Á. Borges-Trenard
AAMADV
Acta Applicandae Mathematicae. An International Survey Journal on Applying Mathematics and Mathematical Applications
G. C.
Shephard
J. A.
Todd

# Finite unitary reflection groups

Canadian J. Math.
1954
6
274–304
MR0059914 (15,600b)
20.0X
H. S. M. Coxeter
M. W.
Short

# The primitive soluble permutation groups of degree less than 256

Springer-Verlag
1992
1519
Lecture Notes in Mathematics

    Berlin

3-540-55501-3
MR1176516 (93g:20006)
20B15 (20B35 20B40 20F16)
A. S. Kondratʹev
x+145
Charles C.
Sims

# Computational methods in the study of permutation groups

Computational Problems in Abstract Algebra (Proc. Conf., Oxford, 1967)
1970
John
Leech
29
Proceedings of a Conference held at Oxford under the auspices of the Science Research Council, Atlas Computer Laboratory
169–183

    Oxford

Pergamon
Oxford67
permutation groups; primitive groups, classification of, stabilizer chain; Schreier Sims
MR0257203 (41 #1856)
20.20 (65.00)
H. Kimura
RUSSIAN translation in: Computations in algebra and number theory (Russian), edited by B. B. Venkov and D. K. Faddeev, pp. 129–147, Matematika, Novoie v Zarubeznoi Naukie, vol. 2, Izdat. MIR, Moscow, 1976
MR 41 # 1856 (H. Kimura), Zbl 215, 100 (J. McKay), CR 11 # 19,829 (G. N. Raney)
Charles C.
Sims

# Computing the order of a solvable permutation group

1990
9
5-6
699–705

Computational group theory, Part 1

0747-7171
MR1075432 (91m:20011)
20B40
Gerhard Hiss
Journal of Symbolic Computation
Charles C.
Sims

# Computation with finitely presented groups

Cambridge University Press
1994
48
Encyclopedia of Mathematics and its Applications

    Cambridge

0-521-43213-8
MR1267733 (95f:20053)
20F05 (20-02 68Q40 68Q42)
Friedrich Otto
xiii+604
Charles C.
Sims

# Computing with subgroups of automorphism groups of finite groups

Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation (Kihei, HI)
1997
Wolfgang
Küchlin
400–403 (electronic)

    New York

The Association for Computing Machinery
ACM

Held in Kihei, HI, July 21–23, 1997

ACM
ISSAC97
MR1810006
68W30 (20D45)

# SOGOS - A Program System for Handling Subgroups of Finite Soluble Groups, version 5.0, User's reference manual

Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule

    Aachen, Germany

1989
groups, finitely presented groups, polycyclic groups, nilpotent groups, p-groups; SOGOS, pc-presentation, ag-presentation, collection, elements, classes of conjugate elements, centralizer, normalizer, normal closure, intersection, sylow subgroups, derived subgroup, series, central series, p-central series, subgroup lattice, table of marks, complements, factor groups; nilpotent quotient (nq); manual
Leonard H.
Soicher

# GRAPE: a system for computing with graphs and groups

Groups and computation (New Brunswick, NJ, 1991)
1993
Larry
Finkelstein
William M.
Kantor
11
DIMACS Ser. Discrete Math. Theoret. Comput. Sci.
287–291

    Providence, RI

Amer. Math. Soc.
DIMACS
0-8218-6599-4
MR1235810
05C85 (20B40)
Bernd
Souvignier

# Irreducible finite integral matrix groups of degree 8 and 10

1994
63
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335–350

With microfiche supplement

0025-5718
MR1213836 (94i:20091)
20H15 (11E12 20C10 20C40)
Alexander W. Mason
MCMPAF
Mathematics of Computation

# SPAS - Subgroup Presentation Algorithms System, version 2.5, User's reference manual

Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule

    Aachen, Germany

1989
SPAS
finitely presented groups; SPAS, subgroup presentation, simplification, low index subgroups; Todd Coxeter (tc), modified Todd Coxeter (mtc), Reidemeister Schreier (rs), reduced Reidemeister Schreier (rrs), Tietze transformations, tree decoding; manual
T. A.
Springer

# Linear algebraic groups

Birkhäuser Boston
1981
9
Progress in Mathematics

    Mass.

3-7643-3029-5
MR632835 (84i:20002)
20-02 (20Gxx)
x+304
John R.
Stembridge

# On the eigenvalues of representations of reflection groups and wreath products

1989
140
2
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0030-8730
MR1023791 (91a:20022)
20C30 (20C15)
A. Kerber
PJMAAI
Pacific Journal of Mathematics
D. E.
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# Pairs of Generators for Matrix Groups. I

The Cayley Bulletin
1987
3
Heiko
Theißen

# Methoden zur Bestimmung der rationalen Konjugiertheit in endlichen Gruppen

Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule
1993
Diplomarbeit

    Aachen, Germany

Heiko
Theißen

# Eine Methode zur Normalisatorberechnung in Permutationsgruppen mit Anwendungen in der Konstruktion primitiver Gruppen

Rheinisch Westfälische Technische Hochschule
1997
Dissertation

    Aachen, Germany

Peter
Thiemann

# SOGOS III - Charaktere und Effizienzuntersuchung

Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule
1987
Diplomarbeit

    Aachen, Germany

Michael R.
Vaughan-Lee

# An aspect of the nilpotent quotient algorithm

Computational group theory (Durham, 1982)
1984
Michael D.
Atkinson
75–83

    London

Academic Press
Durham1982
0-12-066270-1
MR760652 (86b:20040)
20F05 (20-04 20D15 68Q40)
M. F. Newman
Michael R.
Vaughan-Lee

# Collection from the left

1990
9
5-6
725–733

Computational group theory, Part 1

0747-7171
MR1075434 (92c:20065)
20F12 (20-04 20D15 20F18)
M. Greendlinger
Journal of Symbolic Computation
Academic Press
Michael
Vaughan-Lee

# The restricted Burnside problem

The Clarendon Press Oxford University Press
1990
5
London Mathematical Society Monographs. New Series

    New York

, Oxford Science Publications

0-19-853573-2
MR1057610 (92c:20001)
20-02 (20F12 20F40 20F45 20F50)
Norman Blackburn
xiv+209
Robert W.
van der Waall

# On symplectic primitive modules and monomial groups

Nederl. Akad. Wetensch. Proc. Ser. A 79, Indag. Math.
1976
38
4
362–375
MR0424931 (54 #12889)
20D10
T. R. Berger
Stan
Wagon

# Editor's corner: the Euclidean algorithm strikes again

1990
97
2
125–129
0002-9890
MR1041889 (91b:11039)
11E25 (11Y50)
K. S. Williams
AMMYAE
The American Mathematical Monthly
Helmut
Wielandt

# Permutation groups through invariant relations and invariant functions

Department of Mathematics, The Ohio State University
1969
Lecture Notes
Robert A.
Wilson
Peter
Walsh
Jonathan
Tripp
Ibrahim
Suleiman
Richard A.
Parker
Simon P.
Norton
Simon
Nickerson
Steve
Linton
John
Bray
Rachel
Abbott

# ATLAS of Finite Group Representations

http://brauer.maths.qmul.ac.uk/Atlas/
ATLAS
John N.
Bray
Ibrahim A. I.
Suleiman
Peter G.
Walsh
Robert A.
Wilson

# Generating maximal subgroups of sporadic simple groups

2001
29
3
1325–1337
0092-7872
MR1842416 (2002e:20032)
20D08
Hiroyoshi Yamaki
COALDM
Communications in Algebra
Robert A.
Wilson

# Standard generators for sporadic simple groups

1996
184
2
505–515
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MR1409225 (98e:20025)
20D08
JALGA4
Journal of Algebra
Hans
Wondratschek

# Introduction to space-group symmetry

International Tables for Crystallography, Vol. A
Kluwer, Dordrecht
1995
Theo
Hahn
711–735
4th

Space-group symmetry

Hah95
Martin
Wursthorn

# SISYPHOS Computing in modular group algebras, Version 0.5

Math. Inst. B, 3. Lehrstuhl

    Universität Stuttgart

1993
D.
Zagier

# A one-sentence proof that every prime p \equiv 1 \pmod 4 is a sum of two squares

1990
97
2
144
0002-9890
MR1041893 (91b:11040)
11E25
K. S. Williams
AMMYAE
The American Mathematical Monthly
Matthias
Zumbroich

# Grundlagen einer Arithmetik in Kreisteilungskörpern und ihre Implementation in CAS

Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule
1989
Diplomarbeit

    Aachen, Germany

John
Leech

# Computational problems in abstract algebra

1970
29
Proceedings of a Conference held at Oxford under the auspices of the Science Research Council, Atlas Computer Laboratory

    Oxford

Pergamon Press
MR0252149 (40 #5374)
00.04 (10.00)
Computational Problems in Abstract Algebra, Proc. Conf. Oxford, 1967
x+402
MR 40#5374, Zbl 186.299
Michael F.
Newman

# Proceedings of the Second International Conference on the Theory of Groups

1974
372
Lecture Notes in Math.

    Berlin

Springer-Verlag

Held at the Australian National University, Canberra, August 13–24, 1973, With an introduction by B. H. Neumann, Lecture Notes in Mathematics, Vol. 372

MR0344315 (49 #9054)
20-06
Proceedings of the Second International Conference on the Theory of Groups, Canberra, 1973
vii+740
MR 49#9054, Zbl 282.00012
R. A.
Bryce
J.
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Michael F.
Newman

# Group theory

1977
573
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Springer-Verlag

Lecture Notes in Mathematics, Vol. 573

MR0430032 (55 #3040)
20-06
Group theory, Proc. Miniconf., Austral. Nat. Univ., Canberra, 1975
v+146
MR 55#3040, Zbl 342.00008
Jens L.
Mennicke

# Burnside groups

1980
806
Lecture Notes in Mathematics

    Berlin

Springer
3-540-10006-7
MR586041 (81j:20002)
20-06
Proceedings of a Workshop held at the University of Bielefeld, Bielefeld, June–July 1977
ii+274
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Edward W.
Ng

# Symbolic and algebraic computation

1979
72
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Springer-Verlag

EUROSAM '79, an International Symposium held in Marseille, June 1979

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MR575677 (81d:68005)
68-06 (68C20)
xv+557
Michael D.
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# Computational group theory

1984

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Academic Press Inc. [Harcourt Brace Jovanovich Publishers]
0-12-066270-1
MR760641 (85g:20001)
20-06 (68-06)
Proceedings of the London Mathematical Society symposium held in Durham, July 30–August 9, 1982
xii+375
Colin M.
Campbell
Edmund F.
Robertson

# Groups–St. Andrews 1981

1982
71
London Mathematical Society Lecture Note Series

    Cambridge

Cambridge University Press
0-521-28974-2
MR679152 (83j:20005)
20-06
Proceedings of the International Conference on Groups held at the Mathematical Institute, University of St Andrews, St. Andrews, July 25–August 8, 1981
viii+360
Kai Nah
Cheng
Yu Kiang
Leong

# Group theory

1989

    Berlin

Walter de Gruyter & Co.
3-11-011366-X
MR981831 (89j:20001)
20-06
Proceedings of the Singapore Group Theory Conference held at the National University of Singapore, Singapore, June 8–19, 1987
xviii + 586
G. O.
Michler
C. M.
Ringel

# Representation theory of finite groups and finite-dimensional algebras

1991
95
Progress in Mathematics

    Basel

Birkhäuser Verlag
3-7643-2604-2
MR1112154 (91m:20005)
20-06 (00B25 16-06 20Cxx)
Proceedings of the conference held at the University of Bielefeld, Bielefeld, May 15–17, 1991
x+520

# Proceedings of the 1991 International Symposium on Symbolic and Algebraic Computation (ISSAC'91), Bonn 1991

1991
ACM Press
Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC'91), Bonn 1991
Wolfgang
Küchlin

# Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation

1997

    New York

The Association for Computing Machinery
Association for Computing Machinery (ACM)

Held in Kihei, HI, July 21–23, 1997

ACM
MR1809584 (2001i:68010)
68-06 (65-06 68W30)
electronic
Oliver
Gloor

# Proceedings of the 1998 International Symposium on Symbolic and Algebraic Computation

1998

    New York

The Association for Computing Machinery
Association for Computing Machinery (ACM)

Held in Rostock, August 13–15, 1998

ACM
MR1805195 (2001m:68004)
68-06 (00B25 68W30)
front matter+321 pp. (electronic)
Larry
Finkelstein
William M.
Kantor

# Groups and computation

1993
DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 11

    Providence, RI

American Mathematical Society
0-8218-6599-4
MR1235790 (94c:20003)
20-06 (20B40)
Proceedings of the DIMACS Workshop held at Rutgers University, New Brunswick, New Jersey, October 7–10, 1991
xx+313
Larry
Finkelstein
William M.
Kantor

# Groups and computation. II

1997
DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 28

    Providence, RI

American Mathematical Society
0-8218-0516-9
MR1444126 (97m:20003)
20-06 (68-06)
Proceedings of the 2nd DIMACS Workshop held at Rutgers University, New Brunswick, NJ, June 7–10, 1995
xviii+382
William M.
Kantor
Ákos
Seress

# Groups and computation. III

2001
Ohio State University Mathematical Research Institute Publications, 8

    Berlin

Walter de Gruyter & Co.
3-11-016721-2
MR1829467 (2002d:20003)
20-06
Proceedings of the 3rd International Conference held at The Ohio State University, Columbus, OH, June 15–19, 1999
viii+368
Gilbert
Baumslag
David
Epstein
Robert
Gilman
Hamish
Short
Charles
Sims

# Geometric and computational perspectives on infinite groups

1996
DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 25

    Providence, RI

American Mathematical Society
0-8218-0449-9
MR1364175 (96g:20055)
20F32 (20-06)
Proceedings of the Joint DIMACS/Geometry Center Workshop held at the University of Minnesota, Minneapolis, Minnesota, January 3–14, 1994 and Rutgers University, New Brunswick, New Jersey, March 17–20, 1994
xvi+212
Colin M.
Campbell
Thaddeus C.
Hurley
Edmund F.
Robertson
Sean J.
Tobin
James J.
Ward

# Groups '93 Galway/St. Andrews. Vol. 1

1995
211
London Mathematical Society Lecture Note Series

    Cambridge

Cambridge University Press
0-521-47749-2
MR1342775 (96b:20001a)
20-06
Proceedings of the International Conference held at University College, Galway, August 1–14, 1993
xii+304
Colin M.
Campbell
Thaddeus C.
Hurley
Edmund F.
Robertson
Sean J.
Tobin
James J.
Ward

# Groups '93 Galway/St. Andrews. Vol. 2

1995
212
London Mathematical Society Lecture Note Series

    Cambridge

Cambridge University Press
0-521-47750-6
MR1337278 (96b:20001b)
20-06
Proceedings of the International Conference held at University College, Galway, August 1–14, 1993
i–xii and 305–609
Marc
Cabanes

# Finite reductive groups

1997
141
Progress in Mathematics

    Boston, MA

Birkhäuser Boston Inc.

Related structures and representations

0-8176-3885-7
MR1429866 (97i:20001)
20-06 (20G40)
Proceedings of the International Conference held in Luminy, October 3–7, 1994
xii+452

# ISSAC '98: Proceedings of the 1998 international symposium on Symbolic and algebraic computation

1998

    New York, NY, USA

ACM
ACM Press

Chairman: Volker Weispfenning and Barry Trager

1-58113-002-3
Rostock, Germany
ISSAC '98: Proceedings of the 1998 international symposium on Symbolic and algebraic computation
ACM Order No.: 505980, ACM member price $25
J.
Schur

# On the representation of the symmetric and alternating groups by fractional linear substitutions

Internat. J. Theoret. Phys.
2001
40
1
413–458

Translated from the German [J. Reine Angew. Math. 139 (1911), 155–250] by Marc-Felix Otto

0020-7748
MR1820589 (2003a:20016)
20C25 (05E05 20C30)
Tadeusz Józefiak
http://dx.doi.org/10.1023/A:1003772419522
IJTPBM
10.1023/A:1003772419522
International Journal of Theoretical Physics
J.
Schur

# Über die Darstellung der symmetrischen und der alternierenden Gruppe durch gebrochene lineare Substitutionen

Journal für die reine und angewandte Mathematik
1911
139
155–250
http://www.digizeitschriften.de/resolveppn/GDZPPN002167298
42.0154.02
Lukas
Maas

# On a construction of the basic spin representations of symmetric groups

Communications in Algebra
2010
38
4545–4552
http://dx.doi.org/10.1080/00927872.2010.490541
http://arxiv.org/abs/0911.3794
10.1080/00927872.2010.490541
John
Brillhart
D.H.
Lehmer
J.L.
Selfridge

# New primality criteria and factorizations of 2^m \pm 1

Mathematics of Computation
1975
29
620–647
http://dx.doi.org/10.2307/2005583
10.2307/2005583