New characterizations for ICCE-property and p-hypercyclically embedded subgroups

Let [Formula: see text] be a finite group. A subgroup [Formula: see text] of [Formula: see text] is called an ICCE-subgroup of [Formula: see text], if [Formula: see text], where [Formula: see text] is a CAP-embedded subgroup of [Formula: see text] contained in [Formula: see text], which is a generalization of CAP-embedded subgroup and ICC-subgroup. In this paper, we investigate that a normal subgroup is [Formula: see text]-hypercyclically embedded in a finite group [Formula: see text] in which some primary subgroups of [Formula: see text] are ICCE-subgroups of [Formula: see text].