The direct product of a hopfian group with a group with cyclic ccnter

Abstract

In this paper we continue our study of hopficity begun in [1], [2], [3], [4] and [5]. Let A be hopfian and let B have a cyclic center of prime power order. We improve Theorem 4 of [2] by showing that if B has finitely many normal subgroups which form a chain (we say B is n-normal), then AxB is hopfian. We then consider the case when B is a p-group of nilpotency class 2 and show that in certain cases AxB is hopfian.