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

A subgroup H of a group G is said to be an ICΦ-subgroup of G if H ∩ [H,G] ≤ Φ(H). In this paper, based on research work of Kaspczyk, we analyze p-hypercyclically embedded structure of a finite group G under the assumption that some given p-subgroups of G are ICΦ-subgroups of G. Also, all ICΦ-subgroups of symmetric group Sn are determined. [ABSTRACT FROM AUTHOR]