Global Warfield groups

Hunter, Roger; Richman, Fred

doi:10.1090/S0002-9947-1981-0617551-X

Global Warfield groups
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by Roger Hunter and Fred Richman

Trans. Amer. Math. Soc. 266 (1981), 555-572

DOI: https://doi.org/10.1090/S0002-9947-1981-0617551-X

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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 $p$-groups, which includes the classical Ulm-Zippin theory of countable $p$-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.

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