Geodesic
On a~property of Abelian groups related to direct sums and products
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 7, pp. 39-47

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Let $T$ be an infinite set of prime numbers, $\mathcal M$ be a set of groups $\{\mathbb Z(p)\mid p \in T\}$. An Abelian group $A$ is said to be $\mathcal M$-large if $$ \mathrm{Hom}\Bigl(A,\bigoplus_{p\in T}\mathbb Z(p)\Bigr)=\mathrm{Hom}\Bigl(A,\prod_{p\in T}\mathbb Z(p)\Bigr). $$ This paper presents a characterization of $\mathcal M$-large torsion-free and mixed groups. 
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     author = {O. M. Babanskaya (Katerinchuk) and P. A. Krylov},
     title = {On a~property of {Abelian} groups related to direct sums and products},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {39--47},
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     year = {2010},
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O. M. Babanskaya (Katerinchuk); P. A. Krylov. On a~property of Abelian groups related to direct sums and products. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 7, pp. 39-47. http://geodesic.mathdoc.fr/item/FPM_2010_16_7_a1/