The Structure of a Primitive Group

Abstract

In this chapter our focus changes from the combinatorial and ring theoretic representations of permutation groups considered in the last chapter to more direct group theoretic analysis of the groups involved. The point stabilizers of a primitive group form a conjugacy class of maximal subgroups, so classification of primitive groups is closely related to a study of maximal subgroups. Although some of the results in this chapter are valid for infinite groups, the central theorems will apply only to finite groups.