Contents
Preface xi
Part I, Chapter G: General Group Theory
A. Introduction 1
1. Notation 2
2. Some OC-Group Conditions 4
B. Semisimple Subgroups 6
3. Components and the Generalized Fitting Subgroup 6
4. 7r-Components and 7r-Layers 16
5. Lp/-Balance and p*-Groups 23
6. p-Terminally 34
7. Semirigidity 45
8. The Permutation Action of p-Groups on Components 48
C. Nilpotent Groups and Their Extensions 53
9. Modules, Representations, and Cohomology 53
10. Small p-Groups 61
11. Automorphisms of p-Groups and Coprime Action 72
12. p-Constrained Groups 78
13. Solvable Components and Solvable L-Balance 79
14. Goldschmidt-O'Nan Modules 85
D. Fusion and Normal Subgroups 89
15. Abelian Normal Subgroups and Quotients 89
16. Local Control of Fusion 96
E. Uniqueness Subgroups 101
17. Strongly p-Embedded Subgroups and Involutions 101
18. Preuniqueness Subgroups and Standard Components 106
F. The Analysis of Signalizers 110
19. The Bender Method 110
20. The Signahzer Functor Method: /c-Balance 118
21. The Signahzer Functor Method: Signahzer Functors 122
22. The Signahzer Functor Method: Connectivity 125
23. Signalizers, p-Constraint and Transitivity Theorems 129
G. Subgroups of Parabolic Type 134
24. The Klinger-Mason Method 135
25. p-Stability and Quadratic Modules 140
26. Thompson Factorization 147
27. Near Components 157
28. The Amalgam Method 161
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