Finite p-groups in which the cores of all the nonnormal subgroups are in the center

Abstract

Let [Formula: see text] be a finite [Formula: see text]-group. Then [Formula: see text] is said to be a [Formula: see text]-group if [Formula: see text] for every nonnormal subgroup [Formula: see text] of [Formula: see text]. In this paper, we study the [Formula: see text]-group [Formula: see text] and get [Formula: see text]. It is proved that [Formula: see text] if [Formula: see text] and [Formula: see text] if [Formula: see text].