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On extensions of bounded subgroups in Abelian groups. (English) Zbl 1324.20036

Summary: It is well-known that every bounded Abelian group is a direct sum of finite cyclic subgroups. We characterize those non-trivial bounded subgroups \(H\) of an infinite Abelian group \(G\), for which there is an infinite subgroup \(G_0\) of \(G\) containing \(H\) such that \(G_0\) has a special decomposition into a direct sum which takes into account the properties of \(G\), and which induces a natural decomposition of \(H\) into a direct sum of finite subgroups.

MSC:

20K21 Mixed groups
20K27 Subgroups of abelian groups
20K25 Direct sums, direct products, etc. for abelian groups
20K35 Extensions of abelian groups
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