Finite p-Groups G with H′=G′ for Each A2-Subgroup H

Abstract

A finite [Formula: see text]-group [Formula: see text] is called an [Formula: see text]-group if [Formula: see text]is the minimal non-negative integer such that all subgroups of index [Formula: see text] of [Formula: see text] are abelian. The finite [Formula: see text]-groups [Formula: see text] with [Formula: see text] for all [Formula: see text]-subgroups [Formula: see text] of [Formula: see text]are classified completely in this paper. As an application, a problem proposed by Berkovich is solved.