Sylow Subgroups of the Chevalley Groups and Associated (Weakly) Finitary Groups and Rings

Abstract

Automorphisms, isomorphisms and structural descriptions of finitary unitriangular groups over a ring and of Sylow subgroups of Chevalley groups are studied. Also, the theorem on pair unipotent intersections of Chevalley groups has been proved; it is connected with the known question on pair Sylow intersections of finite groups. These investigations use close connections and structural descriptions of considered groups and associated rings, which have been found recently in the case of a commutative ring of coefficients with a strongly maximal ideal. We consider some properties and examples of such ideals.