The local structure of finite groups of characteristic 2 type

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
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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