Finite Group Theory

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Hardcover | 15 November 2000 | Edition Number 2

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Hardcover
320 Pages

Edition Type
Revised

Dimensions(cm)
22.86 x 15.24 x 2.24

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During the last 40 years the theory of finite groups has developed dramatically. The finite simple groups have been classified and are becoming better understood. Tools exist to reduce many questions about arbitrary finite groups to similar questions about simple groups. Since the classification there have been numerous applications of this theory in other branches of mathematics. Finite Group Theory develops the foundations of the theory of finite groups. It can serve as a text for a course on finite groups for students already exposed to a first course in algebra. It could supply the background necessary to begin reading journal articles in the field. For specialists it also provides a reference on the foundations of the subject. This second edition has been considerably improved with a completely rewritten Chapter 15 considering the 2-Signalizer Functor Theorem, and the addition of an appendix containing solutions to exercises.

Industry Reviews

'I consider this book as an extremely valuable source and help for anyone interested in a serious study of finite groups.' U. Dempwolff, Zentralblatt MATH

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Preface	p. vii
Preliminary results	p. 1
Elementary group theory	p. 1
Categories	p. 6
Graphs and geometries	p. 8
Abstract representations	p. 9
Permutation representations	p. 13
Permutation representations	p. 13
Sylow's Theorem	p. 19
Representations of groups on groups	p. 22
Normal series	p. 22
Characteristic subgroups and commutators	p. 25
Solvable and Nilpotent groups	p. 27
Semidirect products	p. 29
Central products and wreath products	p. 32
Linear representations	p. 35
Modules over the group ring	p. 35
The general linear group and special linear group	p. 42
The dual representation	p. 46
Permutation groups	p. 53
The symmetric and alternating groups	p. 53
Rank 3 permutation groups	p. 59
Extensions of groups and modules	p. 64
1-cohomology	p. 64
Coprime action	p. 70
Spaces with forms	p. 75
Bilinear, sesquilinear, and quadratic forms	p. 75
Witt's Lemma	p. 81
Spaces over finite fields	p. 85
The classical groups	p. 88
p-groups	p. 105
Extremal p-groups	p. 105
Coprime action on p-groups	p. 112
Change of field of a linear representation	p. 117
Tensor products	p. 117
Representations over finite fields	p. 123
Minimal polynomials	p. 126
Presentations of groups	p. 138
Free groups	p. 138
Coxeter groups	p. 141
Root systems	p. 148
The generalized Fitting subgroup	p. 156
The generalized Fitting subgroup	p. 157
Thompson factorization	p. 162
Central extensions	p. 166
Linear representations of finite groups	p. 177
Characters in coprime characteristic	p. 178
Characters in characteristic zero	p. 181
Some special actions	p. 192
Transfer and fusion	p. 197
Transfer	p. 197
Alperin's Fusion Theorem	p. 200
Normal p-complements	p. 202
Semiregular action	p. 205
The geometry of groups of Lie type	p. 208
Complexes	p. 208
Buildings	p. 214
BN-pairs and Tits systems	p. 217
Signalizer functors	p. 228
Solvable signalizer functors	p. 228
Finite simple groups	p. 241
Involutions in finite groups	p. 242
Connected groups	p. 244
The finite simple groups	p. 249
An outline of the Classification Theorem	p. 258
References	p. 267
List of Symbols	p. 269
Index	p. 271
Table of Contents provided by Syndetics. All Rights Reserved.

Finite Group Theory

At a Glance

Hardcover

Industry Reviews

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