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The Local Structure of Finite Groups of Characteristic 2 Type
Daniel Gorenstein and Richard Lyons
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Memoirs of the American Mathematical Society
1983; 731 pp; softcover
Volume: 42
ISBN-10: 0-8218-2276-4
ISBN-13: 978-0-8218-2276-0
List Price: US$83
Individual Members: US$49.80
Institutional Members: US$66.40
Order Code: MEMO/42/276
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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

Part I: Properties of \(K\)-groups and Preliminary Lemmas
  • Introduction
  • Decorations of the known simple groups
  • Local subgroups of the known simple groups
  • Balance and signalizers
  • Generational properties of \(K\)-groups
  • Factorizations
  • Miscellaneous general results and lemmas about \(K\)-groups
  • Appendix by N. Burgoyne
Part II: The Trichotomy Theorem
  • Odd standard form
  • Signalizer functors and weak proper \(2\)-generated \(p\)-cores
  • Almost strongly \(p\)-embedded maximal \(2\)-local subgroups
  • References
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