ON NEARLY CAP-EMBEDDED SUBGROUPS OF FINITE GROUPS

Abstract

We introduce a new subgroup embedding property of a finite group called nearly CAP-embedded subgroup.  Using this subgroup property, we determine the structure of finite groups with some nearly CAP-embedded subgroups of Sylow subgroups.  Our results unify and generalize some recent theorems on p-nilpotency and supersolvability of finite groups.