On extensions of bounded subgroups in Abelian groups

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Abstract

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 G0 of G containing H such that G0 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.

Original languageEnglish
Pages (from-to)175-188
Number of pages14
JournalCommentationes Mathematicae Universitatis Carolinae
Volume55
Issue number2
StatePublished - 1 Jan 2014

Keywords

  • Abelian group
  • Bounded group
  • Simple extension

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