A PROBLEM ON ABELIAN GROUPS
Copyright policy )A PROBLEM ON ABELIAN GROUPS
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.
tensor product closed class, Direct sums, direct products, etc. for abelian groups, Subgroups of abelian groups, Extensions of abelian groups, Fuchs-44 groups, reduced groups, direct sum of p-primary groups
tensor product closed class, Direct sums, direct products, etc. for abelian groups, Subgroups of abelian groups, Extensions of abelian groups, Fuchs-44 groups, reduced groups, direct sum of p-primary groups
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