On the ICCE-property of finite groups

Let [Formula: see text] be a finite group and [Formula: see text] a subgroup of [Formula: see text]. Then [Formula: see text] is said to be a [Formula: see text]-embedded subgroup of [Formula: see text] if, for each prime [Formula: see text] dividing the order of [Formula: see text], there exists a [Formula: see text]-subgroup [Formula: see text] of [Formula: see text] such that a Sylow [Formula: see text]-subgroup of [Formula: see text] is also a Sylow [Formula: see text]-subgroup of [Formula: see text]; [Formula: see text] is called an [Formula: see text]-subgroup of [Formula: see text], if [Formula: see text], where [Formula: see text] is a [Formula: see text]-subgroup of [Formula: see text] contained in [Formula: see text]. We say that [Formula: see text] is an [Formula: see text]-subgroup of [Formula: see text], if [Formula: see text], where [Formula: see text] is a [Formula: see text]-embedded subgroup of [Formula: see text] contained in [Formula: see text], which is a generalization of [Formula: see text]-embedded subgroup and [Formula: see text]-subgroup. In this paper, we investigate the structure of finite groups under the assumption that some primary subgroups have [Formula: see text]-property and some further results are obtained.