Contents
Preface xiii
PART II, CHAPTERS 1-4: UNIQUENESS THEOREMS
Chapter 1. General Lemmas 1
1. Uniqueness Elements 1
2. Permutation Groups 3
3. Two Theorems on Doubly Transitive Groups 7
4. Miscellaneous Lemmas 12
Chapter 2. Strongly Embedded Subgroups and Related Conditions on
Involutions 19
1. Introduction and Statement of Results 19
2. The Subsidiary Theorems 25
3. The Basic Setup and Counting Arguments 27
4. Reduction to the Simple Case: Theorem 1 33
5. p-Subgroups Fixing Two or More Points: Theorem 2 38
6. A Reduction: Corollary 3 42
7. Double Transitivity and I
a
^ z : Theorem 4 44
8. Reductions for Theorem SE 50
9. Good Subgroups of V Exist 54
10. The Structures of V and D 58
11. Proof of Theorem 6 (and Theorem SE) 62
12. The Group L = (z,t, [02(D),t]) 65
13. The Unitary Case 72
14. The Suzuki Case 74
15. The Linear Case 79
16. The Structure of D and Cx(u) 82
17. The Proof of Theorem ZD 88
18. The Weak 2-Generated 2-Core 91
19. The J2 Case 95
20. Bender Groups as 2-Components 98
21. Theorem SU: The 2-Central Case 101
22. The Ji Case 103
23. The 2A9 Case 105
24. Theorem SA: Strongly Closed Abelian 2-Subgroups 109
25. Theorem SF: Terminal Bender Components 112
26. Theorem SF: Product Disconnection 119
27. Theorem ,49 127
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