Subgroups of Simple Algebraic Groups and of Related Finite and Locally Finite Groups of Lie Type

Abstract

This is a survey of some recent results on the subgroup structure of simple algebraic groups and of related finite and locally finite groups of Lie type. The first section contains basic material on simple algebraic groups, their automorphisms and Frobenius morphisms, and shows how every finite or locally finite group of Lie type can be realised as the fixed point group G σ or G ϕ , of a suitable automorphism σ or ϕ of a simple algebraic group G. The other two sections deal with classical groups and exceptional groups. Both sections start with results on the closed subgroups of G, and then show how these results can be used to deduce corresponding results about the subgroups of G σ and G ϕ .