Murley groups and the torsion-freeness of Ext

Abstract

Let B be a torsion-free Abelian group of finite rank with OT(B) = type(Q). This paper gives necessary and sufficient conditions for such a group B to be a finitely faithful S-group with the property that every finite rank pure subgroup of a group A with Ext( A, B) torsion-free is B-cobalanced in A. Several applications of this result are given. In particular, we classify the torsion-free groups A of finite rank such that Ext ( A, B) is torsion-free in the case that B is an irreducible Murley group.