Contents
Preface ix
PART IV: THE SPECIAL ODD CASE
Chapter 1. General Introduction to the Special Odd Case 1
1. The Goals: Theorems C2 and C3 1
2. Theorems C2 and 6^ 2
3. General Comments on the Proof of Theorem C2 6
4. Theorem C3 and Its Proof 9
Chapter 2. General Lemmas 13
1. The Bender/Glauberman Method 13
2. p-Groups and Coprime Action 18
3. Transfer and Fusion 28
4. 2-Components and 2-Groups 32
5. Pumpups and 2-Terminality 35
6. Terminality 37
7. Semirigidity 38
8. Preuniqueness Subgroups 43
9. Signalizer Functors and Balance 48
10. Ordinary Character Theory 48
11. Modular Character Theory 51
12. £N-Pairs 56
13. Number Theory 58
14. Miscellaneous 58
Chapter 3. Theorem 6^: Stage 1 61
1. Introduction 61
2. The 2-Rank 2 Case: Alperin's Theorem 64
3. Theorem 2: 2-Terminal 2-Components of 2-Rank 1 67
4. The Fusion of z and Structure of Q 67
5. Involutory /-Automorphisms 71
6. Elimination of /-Automorphisms 75
7. Theorem 3: The Nonfused Case 77
8. Theorem 3: The Fused Case 80
9. Theorem 4: 2-Terminal 2-Components of 2-Rank 2 86
10. The O'N Case 90
11. Theorem 5 93
12. Groups of 2-Rank 3 94
13. 2-Groups of Type M12 99
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