Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Global Warfield groups


Authors: Roger Hunter and Fred Richman
Journal: Trans. Amer. Math. Soc. 266 (1981), 555-572
MSC: Primary 20K21
DOI: https://doi.org/10.1090/S0002-9947-1981-0617551-X
MathSciNet review: 617551
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 20K21

Retrieve articles in all journals with MSC: 20K21


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1981-0617551-X
Article copyright: © Copyright 1981 American Mathematical Society