Descripciones mejoradas de Syndetics:

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.

Tabla de contenidos provista por Syndetics

• Preface(p. vii)
• 1 Preliminary results(p. 1)
• 1 Elementary group theory(p. 1)
• 2 Categories(p. 6)
• 3 Graphs and geometries(p. 8)
• 4 Abstract representations(p. 9)
• 2 Permutation representations(p. 13)
• 5 Permutation representations(p. 13)
• 6 Sylow's Theorem(p. 19)
• 3 Representations of groups on groups(p. 22)
• 7 Normal series(p. 22)
• 8 Characteristic subgroups and commutators(p. 25)
• 9 Solvable and Nilpotent groups(p. 27)
• 10 Semidirect products(p. 29)
• 11 Central products and wreath products(p. 32)
• 4 Linear representations(p. 35)
• 12 Modules over the group ring(p. 35)
• 13 The general linear group and special linear group(p. 42)
• 14 The dual representation(p. 46)
• 5 Permutation groups(p. 53)
• 15 The symmetric and alternating groups(p. 53)
• 16 Rank 3 permutation groups(p. 59)
• 6 Extensions of groups and modules(p. 64)
• 17 1-cohomology(p. 64)
• 18 Coprime action(p. 70)
• 7 Spaces with forms(p. 75)
• 19 Bilinear, sesquilinear, and quadratic forms(p. 75)
• 20 Witt's Lemma(p. 81)
• 21 Spaces over finite fields(p. 85)
• 22 The classical groups(p. 88)
• 8 p-groups(p. 105)
• 23 Extremal p-groups(p. 105)
• 24 Coprime action on p-groups(p. 112)
• 9 Change of field of a linear representation(p. 117)
• 25 Tensor products(p. 117)
• 26 Representations over finite fields(p. 123)
• 27 Minimal polynomials(p. 126)
• 10 Presentations of groups(p. 138)
• 28 Free groups(p. 138)
• 29 Coxeter groups(p. 141)
• 30 Root systems(p. 148)
• 11 The generalized Fitting subgroup(p. 156)
• 31 The generalized Fitting subgroup(p. 157)
• 32 Thompson factorization(p. 162)
• 33 Central extensions(p. 166)
• 12 Linear representations of finite groups(p. 177)
• 34 Characters in coprime characteristic(p. 178)
• 35 Characters in characteristic zero(p. 181)
• 36 Some special actions(p. 192)
• 13 Transfer and fusion(p. 197)
• 37 Transfer(p. 197)
• 38 Alperin's Fusion Theorem(p. 200)
• 39 Normal p-complements(p. 202)
• 40 Semiregular action(p. 205)
• 14 The geometry of groups of Lie type(p. 208)
• 41 Complexes(p. 208)
• 42 Buildings(p. 214)
• 43 BN-pairs and Tits systems(p. 217)
• 15 Signalizer functors(p. 228)
• 44 Solvable signalizer functors(p. 228)
• 16 Finite simple groups(p. 241)
• 45 Involutions in finite groups(p. 242)
• 46 Connected groups(p. 244)
• 47 The finite simple groups(p. 249)
• 48 An outline of the Classification Theorem(p. 258)
• References(p. 267)
• List of Symbols(p. 269)
• Index(p. 271)