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Book Cover
E-book
Author Gorenstein, Daniel, author

Title The local structure of finite groups of characteristic 2 type / Daniel Gorenstein and Richard Lyons
Published Providence, Rhode Island : American Mathematical Society, [1983]
©1983

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Description 1 online resource (742 pages)
Series Memoirs of the American Mathematical Society, 0065-9266 ; number 276
Memoirs of the American Mathematical Society ; no. 276.
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
Bibliography Includes bibliographical references (pages 723-731)
Notes English
Print version record
Subject Finite simple groups.
Finite simple groups
Form Electronic book
Author Lyons, Richard, 1945- author.
ISBN 9781470406868
1470406861