On ICΦ-subgroups and p-hypercyclically embedded structure of finite groups

A subgroup Formula: see text of a group Formula: see text is said to be an Formula: see text-subgroup of Formula: see text if Formula: see text. In this paper, based on research work of Kaspczyk, we analyze Formula: see text-hypercyclically embedded structure of a finite group Formula: see text under the assumption that some given Formula: see text-subgroups of Formula: see text are Formula: see text-subgroups of Formula: see text. Also, all Formula: see text-subgroups of symmetric group Formula: see text are determined.