Author(s): M. Aschbacher
Series: Cambridge Studies in Advanced Mathematics 10
Edition: 2
Publisher: Cambridge University Press
Year: 2000
Language: English
Pages: 314
Preface......Page 7
1 Elementary group theory ......Page 11
2 Categories ......Page 16
3 Graphs and geometries ......Page 17
4 Abstract representations ......Page 19
5 Permutation representations ......Page 23
6 Sylow's Theorem ......Page 29
7 Normal series ......Page 32
8 Characteristic subgroups and commutators ......Page 35
9 Solvable and nilpotent groups ......Page 37
10 Semidirect products ......Page 39
11 Central products and wreath products ......Page 42
12 Modules over the group ring ......Page 45
13 The general linear group and special linear group ......Page 52
14 The dual representation ......Page 56
15 The symmetric and alternating groups ......Page 63
16 Rank 3 permutation groups ......Page 69
17 1-cohomology ......Page 74
18 Coprime action ......Page 80
19 Bilinear, sesquilinear, and quadratic forms ......Page 85
20 Witt's Lemma ......Page 91
21 Spaces over finite fields ......Page 95
22 The classical groups ......Page 98
23 Extremal p-groups ......Page 115
24 Coprime action on p-groups ......Page 122
25 Tensor products ......Page 127
26 Representations over finite fields ......Page 133
27 Minimal polynomials ......Page 137
28 Free groups ......Page 148
29 Coxeter groups ......Page 151
30 Root systems ......Page 158
11 The generalized Fitting subgroup ......Page 166
31 The generalized Fitting subgroup ......Page 167
32 Thompson factorization ......Page 172
33 Central extensions ......Page 176
12 Linear representations of finite groups ......Page 187
34 Characters in coprime characteristic ......Page 188
35 Characters in characteristic 0 ......Page 191
36 Some special actions ......Page 202
37 Transfer ......Page 207
38 Alperin's Fusion Theorem ......Page 210
39 Normal p-complements ......Page 212
40 Semiregular action ......Page 215
41 Complexes ......Page 219
42 Buildings ......Page 225
43 BN-pairs and Tits systems ......Page 228
44 Solvable signalizer functors ......Page 239
16 Finite simple groups ......Page 252
45 Involutions in finite groups ......Page 253
46 Connected groups ......Page 255
47 The finite simple groups ......Page 259
48 An outline of the Classification Theorem ......Page 270
Appendix ......Page 279
References ......Page 307
List of Symbols ......Page 309
Index ......Page 311
