Contents
Preface xi
Background and overview 1
Chapter 0. Introduction 3
0.1. The Classification Theorem 3
0.2. Principle I: Recognition via local subgroups 4
0.3. Principle II: Restricted structure of local subgroups 7
0.4. The finite simple groups 16
0.5. The Classification grid 19
Chapter 1. Overview: The classification of groups of Gorenstein-Walter type 25
The Main Theorem for groups of Gorenstein-Walter type 25
1.1. A strategy based on components in centralizers 26
1.2. The Odd Order Theorem 28
1.3. (Level 1) The Strongly Embedded Theorem
and the Dichotomy Theorem 29
1.4. The 2-Rank 2 Theorem 33
1.5. (Level 1) The Sectional 2-Rank 4 Theorem
and the 2-Generated Core Theorem 35
1.6. The B-Conjecture and the Standard Component Theorem 41
1.7. The Unbalanced Group Theorem, the 2An-Theorem,
and the Classical Involution Theorem 44
1.8. Finishing the Unbalanced Group Theorem and the B-Theorem 48
1.9. The Odd Standard Component Theorem
and the Aschbacher-Seitz reduction 53
1.10. The Even Standard Component Theorem 55
Summary: Statements of the major subtheorems 59
Chapter 2. Overview: The classification of groups of characteristic 2 type 63
The Main Theorem for groups of characteristic 2 type 63
2.1. The Quasithin Theorem covering e(G) 2 65
2.2. The trichotomy approach to treating e(G) 3 66
2.3. The Trichotomy Theorem for e(G) 4 69
2.4. The e(G) = 3 Theorem (including trichotomy) 75
2.5. The Standard Type Theorem 77
2.6. The GF (2) Type Theorem 77
2.7. The Uniqueness Case Theorem 78
Conclusion: The proof of the Characteristic 2 Type Theorem 80
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