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The Local Structure of Finite Groups of Characteristic 2 Type
 
The Local Structure of Finite Groups of Characteristic 2 Type
eBook ISBN:  978-1-4704-0686-8
Product Code:  MEMO/42/276.E
List Price: $88.00
MAA Member Price: $79.20
AMS Member Price: $52.80
The Local Structure of Finite Groups of Characteristic 2 Type
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The Local Structure of Finite Groups of Characteristic 2 Type
eBook ISBN:  978-1-4704-0686-8
Product Code:  MEMO/42/276.E
List Price: $88.00
MAA Member Price: $79.20
AMS Member Price: $52.80
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 421983; 731 pp
    MSC: Primary 20;

    In this Memoir, Gorenstein and Lyons study the generic finite simple group of characteristic 2 type whose proper subgroups are of known type. Their principal result (the Trichotomy Theorem) asserts that such a group has one of three precisely determined internal structures. (Simple groups with these structures have been classified by several authors.) The proof is completely local-theoretic and, in particular, depends crucially on signalizer functor theory. It also depends on a large number of properties of the known finite simple groups. The development of some of these properties is a contribution to the general theory of the known groups.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • Part I. Properties of $K$-groups, and preliminary lemmas
    • 2. Decorations of the known simple groups
    • 3. Local subgroups of the known simple groups
    • 4. Balance and signalizers
    • 5. Generational properties of $K$-groups
    • 6. Factorizations
    • 7. Miscellaneous general results and lemmas about $K$-groups
    • Appendix
    • Part II. The trichotomy theorem
    • 1. Odd standard form
    • 2. Signalizer functors and weak proper 2-generated $p$-cores
    • 3. Almost strongly $p$-embedded maximal 2-local subgroups
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 421983; 731 pp
MSC: Primary 20;

In this Memoir, Gorenstein and Lyons study the generic finite simple group of characteristic 2 type whose proper subgroups are of known type. Their principal result (the Trichotomy Theorem) asserts that such a group has one of three precisely determined internal structures. (Simple groups with these structures have been classified by several authors.) The proof is completely local-theoretic and, in particular, depends crucially on signalizer functor theory. It also depends on a large number of properties of the known finite simple groups. The development of some of these properties is a contribution to the general theory of the known groups.

  • Chapters
  • 1. Introduction
  • Part I. Properties of $K$-groups, and preliminary lemmas
  • 2. Decorations of the known simple groups
  • 3. Local subgroups of the known simple groups
  • 4. Balance and signalizers
  • 5. Generational properties of $K$-groups
  • 6. Factorizations
  • 7. Miscellaneous general results and lemmas about $K$-groups
  • Appendix
  • Part II. The trichotomy theorem
  • 1. Odd standard form
  • 2. Signalizer functors and weak proper 2-generated $p$-cores
  • 3. Almost strongly $p$-embedded maximal 2-local subgroups
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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