(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 7, PAGES 39-47

## On a property of Abelian groups related to direct sums and products

O. M. Babanskaya (Katerinchuk)
P. A. Krylov

Abstract

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Let $T$ be an infinite set of prime numbers, $\mathcal M$ be a set of groups $\left\{$Z(p) | p Î T}. An Abelian group $A$ is said to be $\mathcal M$-large if

$\Hom \left( A, \bigoplus_\left\{p \in T\right\} \mathbb Z\left(p\right) \right) = \Hom \left( A, \prod_\left\{p \in T\right\} \mathbb Z\left(p\right) \right).$

This paper presents a characterization of $\mathcal M$-large torsion-free and mixed groups.

Location: http://mech.math.msu.su/~fpm/eng/k10/k107/k10702h.htm