Abstract

A subgroup [Formula: see text] of a group [Formula: see text] is called an [Formula: see text]-subgroup of [Formula: see text] if there exists a normal subgroup [Formula: see text] of [Formula: see text] such that [Formula: see text] and [Formula: see text] for all [Formula: see text]. In this paper, we obtain new criteria for a normal subgroup to be contained in the [Formula: see text]-hypercenter of a finite group by assuming that some of its subgroups are [Formula: see text]-subgroups. Our results generalize and uniform many known results.

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