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

• 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

• Odd standard form
• Signalizer functors and weak proper \(2\)-generated \(p\)-cores
• Almost strongly \(p\)-embedded maximal \(2\)-local subgroups
• References