On a property of Abelian groups related to direct sums and products |
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Authors: | O M Babanskaya P A Krylov |
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Institution: | 1. Tomsk State University, Tomsk, Russia
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Abstract: | Let T be an infinite set of prime numbers, $ \mathcal{M} $ be a set of groups $ \left\{ {\left. {\mathbb{Z}(p)} \right|p \in T} \right\} $ . An Abelian group A is said to be $ \mathcal{M} $ -large if $$ {\text{Hom}}\left( {A,\mathop { \bigoplus }\limits_{p \in T} \mathbb{Z}(p)} \right) = {\text{Hom}}\left( {A,\prod\limits_{p \in T} {\mathbb{Z}(p)} } \right). $$ This paper presents a characterization of $ \mathcal{M} $ -large torsion-free and mixed groups. |
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