Quasipure injective torsion-free groups with indecomposable pure subgroups

In a quasipure injective torsion-free Abelian group whose pure subgroups are strongly indecomposable, any nonzero endomorphism is shown to be a monomorphism. The results of this paper together with results obtained earlier describe quasipure injective torsion-free groups. As a corollary, it is proved that any quasipure injective torsion-free group is transitive. Translated fromMatematicheskie Zametki, Vol. 68, No. 4, pp. 587–592, October, 2000.