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The Local Structure of Finite Groups of Characteristic 2 Type
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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$88 Individual Members: US$52.80
Institutional Members: US\$70.40
Order Code: MEMO/42/276

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.

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