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The local structure of finite...
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The local structure of finite groups of characteristic 2 type / Daniel Gorenstein and Richard Lyons.
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Bibliographic Details
Main Authors:
Gorenstein, Daniel
(Author)
,
Lyons, Richard, 1945-
(Author)
Format:
eBook
Language:
English
Published:
Providence, Rhode Island :
American Mathematical Society,
[1983]
Series:
Memoirs of the American Mathematical Society ;
no. 276.
Subjects:
Finite simple groups.
Finite simple groups
Online Access:
Click for online access
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Description
Table of Contents
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Table of Contents:
Table of Contents
Acknowledgements
General Introduction
Part I: Properties of K-groups and Preliminary Lemmas
Chapter 1. Introduction
1. Notation
2. p-layers
3. The known simple groups
4. Preliminaries concerning groups of Lie type
5. Basic properties of the sporadic groups
Chapter 2. Decorations of the known simple groups
6. Schur multipliers and covering groups of the known simple groups
7. Automorphisms of the known simple groups
Chapter 3. Local subgroups of the known simple groups.
8. The local structure of classical groups, as seen on their natural modules
9. Outer automorphisms of Chevalley groups
10. Sylow structure, p-rank, and 2-local p-rank of the known simple groups
11. The permutation action of large elementary abelian p-groups on p-components of K-groups
12. p-fusion in the known simple groups
13. Parabolic subgroups of Chevalley groups
14. Subcomponents and pumpups of the known simple groups
15. Action of commuting p-elements on subcomponents of known simple groups
16. Splitting primes for groups in Chev (2)
17. Standard subcomponents of groups in Chev (2)
Chapter 4. Balance and signalizers
18. L[sub(p)], -balance and related results
19. Local and global balance
20. Signalizers in the known simple groups
21. Signalizer functors
Chapter 5. Generational properties of K-groups
22. Generation
23. Generation of K-groups
24. Strongly p-embedded subgroups and proper k-generated cores in K-groups
25. Generation of pumpups of the known simple groups
26. Existence of layers
27. Balance vs. generation
Chapter 6. Factorizations
28. Factorizations in K-groups.
Chapter 7. Miscellaneous general results and lemmas about K-groups
29. Groups with self-centralizing elementary abelian subgroups of low rank
30. Miscellaneous special lemmas
31. p-groups and connectedness
32. Miscellaneous general lemmas
33. The fundamental property of groups of characteristic 2 type
Appendix
34. Elements of order 3 in Chevalley groups of characteristic 2
Part II: The Trichotomy Theorem
Chapter 1. Odd standard form
1. Introduction
2. A preliminary lemma
3. The p-constrained case
4. Maximal p-components
5. Partial standard form.
6. The characteristic of L
7. The alternating case
8. The sporadic case
9. Quasisimplicity
10. The embedding of B: field automorphisms
11. The embedding of B: splitting and half-splitting primes
12. Neighbors
13. Coda
Chapter 2. Signalizer functors and weak proper 2-generated p- cores
1. Introduction
2. Balance
3. The p- components of 1[sub(b)]
4. Signalizer functors and pre-uniqueness subgroups
5. Case (IV): existence of extremal elements of B[sup(1)][sub(max)] (G
3)
6. Case (IV): some properties of extremal elements.
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