Finite groups with some CAP-subgroups

Abstract

A subgroup $A$ of a group $G$ is said to be a CAP-subgroup of $G$ if for any chief factor $H/K$ of $G$, there holds $H\cap A=K\cap A$ or $HA=KA$. We investigate the influence of CAP-subgroups on the structure of finite groups. Some recent results are generalized.