Abelian groups whose nonzero endomorphisms have nonessential kernels

Abstract

In this paper we describe completely the -singular subgroup of an abelian group and a -nonsingular abelian group in terms of the basic subgroups of its p-components and the quotient group by the torsion part. We also prove that a pure subgroup and a quotient group by a pure subgroup of a -nonsingular abelian group are -nonsingular and give a condition under which a pure extension of a -nonsingular abelian group by a -nonsingular group is -nonsingular. © 2017 Elsevier B.V. All rights reserved.