A note on ICΦ-subgroups of finite groups

Let [Formula: see text] be a finite group. A subgroup [Formula: see text] of [Formula: see text] is said to be an [Formula: see text]-subgroup of [Formula: see text] if [Formula: see text]. In this paper, we shall obtain some characterizations about [Formula: see text]-nilpotent and [Formula: see text]-hypercyclically embedded structure of [Formula: see text] under the assumption that certain some subgroups of [Formula: see text] are [Formula: see text]-subgroups of [Formula: see text].