Global Warfield groups

Abstract

A global Warfield group is a summand of a simply presented abelian group. The theory of global Warfield groups encompasses both the theory of totally projective p p -groups, which includes the classical Ulm-Zippin theory of countable p p -groups, and the theory of completely decomposable torsion-free groups. This paper develops the central results of the theory including existence and uniqueness theorems. In addition it is shown that every decomposition basis of a global Warfield group has a nice subordinate with simply presented torsion cokernel, and that every global Warfield group is a direct sum of a group of countable torsion-free rank and a simply presented group.