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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

An application of set theory to the torsion product of abelian groups


Author: Patrick Keef
Journal: Proc. Amer. Math. Soc. 118 (1993), 735-738
MSC: Primary 20K10; Secondary 03E75, 20K40
DOI: https://doi.org/10.1090/S0002-9939-1993-1146863-2
MathSciNet review: 1146863
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Abstract: The following problem of Fuchs is considered: relate the abelian groups $ A$ and $ B$ assuming $ \operatorname{Tor} (A,G) \cong \operatorname{Tor} (B,G)$ for all reduced abelian groups $ G$. A complete characterization is obtained in any set-theoretic universe in which $ E(\kappa )$ is valid for a proper class of regular cardinals $ \kappa $.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1146863-2
Keywords: Abelian $ p$-group, torsion product
Article copyright: © Copyright 1993 American Mathematical Society