The influence of ICΦ-subgroups on the structure of finite groups.

A subgroup H of a group G is called an I C Φ -subgroup of G if H ∩ [ H , G ] ≤ Φ (H) . We investigate the structure of a finite group G under the assumption that some subgroups of G are I C Φ -subgroups of G, and some results of p-nilpotency and supersolvability of finite groups are obtained. [ABSTRACT FROM AUTHOR]