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.