Geodesic
A~problem on Abelian groups
Sbornik. Mathematics, Tome 34 (1978) no. 4, pp. 461-474

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We solve Problem 44 in the book by L. Fuchs “Infinite Abelian Groups”, Vol. I, which asks for a classification of the groups $G$ having the following property: if $G$ is contained in the direct sum of reduced groups, then $nG$ for some $n>0$ is contained in a finite direct sum of these groups. A group has this property if and only if it has no unbounded factor groups that are direct sums of periodic cyclic groups. We also consider a generalization of this problem, when instead of the class of all reduced groups we take an arbitrary class of groups. We derive a number of properties of such groups. Bibliography: 8 titles. 
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     author = {A. V. Ivanov},
     title = {A~problem on {Abelian} groups},
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A. V. Ivanov. A~problem on Abelian groups. Sbornik. Mathematics, Tome 34 (1978) no. 4, pp. 461-474. http://geodesic.mathdoc.fr/item/SM_1978_34_4_a3/