On the capability of finite p-groups with derived subgroup of order p

Abstract

A group is said to be capable if it is a central factor group. Let denotes the class of finite p-groups with derived subgroup of order p and central factor group of order p2. In this paper for groups in , we compute the various homological functors, among them the nonabelian tensor square and the Schur multiplier. Furthermore, the epicenters of all these groups are determined to give a complete classification of finite capable p-groups with derived subgroup of order p.