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This article is cited in 26 scientific papers (total in 26 papers)
A problem on Abelian groups
A. V. Ivanov
Abstract:
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.
Received: 03.06.1977
Citation:
A. V. Ivanov, “A problem on Abelian groups”, Mat. Sb. (N.S.), 105(147):4 (1978), 525–542; Math. USSR-Sb., 34:4 (1978), 461–474
Linking options:
https://www.mathnet.ru/eng/sm2538https://doi.org/10.1070/SM1978v034n04ABEH001220 https://www.mathnet.ru/eng/sm/v147/i4/p525
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Abstract page: | 347 | Russian version PDF: | 103 | English version PDF: | 14 | References: | 54 |
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