FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(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 {Z(p) | p Î T}. An Abelian group A is said to be $ \mathcal M $-large if

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

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

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