THE P-INTERSECTION SUBGROUPS IN QUASI-SIMPLE AND ALMOST SIMPLE FINITE-GROUPS

Let p be a fixed prime and G a finite group. A proper subgroup X < G i s called a p-intersection subgroup if X boolean AND X-8 is a p-group f or each g is an element of G\X, but X is not a p-group. In this paper we classify the p-intersection subgroups in the quasi-simple and almos t simple finite groups. (C) 1998 Academic Press.