Torsion-free Abelian groups with cyclic p-basic subgroups

We investigate the structure of indecomposable torsion-free Abelian groups all of whose p-basic subgroups are cyclic, and also the structure of the groups and rings of endomorphisms of such groups. We prove the existence of a torsion-free Abelian group of countable rank with cyclic p-basic subgroups which has no indecomposable nonzero direct summands.Translated from Matematicheskie Zametki, Vol. 20, No. 6, pp. 805–813, December, 1976.