Thep-Intersection Subgroups in Quasi-Simple and Almost Simple Finite Groups

Letpbe a fixed prime andGa finite group. A proper subgroupX < Gis called ap-intersection subgroupifX ∩ Xgis ap-group for eachg G\X, butXis not ap-group. In this paper we classify thep-intersection subgroups in the quasi-simple and almost simple finite groups.