Characterization of almost maximally almost-periodic groups

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8 Scopus citations


Let G be an Abelian group. We prove that a group G admits a Hausdorff group topology τ such that the von Neumann radical n (G, τ) of (G, τ) is non-trivial and finite iff G has a non-trivial finite subgroup. If G is a topological group, then n (n (G)) ≠ n (G) if and only if n (G) is not dually embedded. In particular, n (n (Z, τ)) = n (Z, τ) for any Hausdorff group topology τ on Z.

Original languageEnglish
Pages (from-to)2214-2219
Number of pages6
JournalTopology and its Applications
Issue number13
StatePublished - 1 Aug 2009


  • Almost maximally almost-periodic
  • Characterized group
  • Dually embedded
  • T-sequence
  • von Neumann radical

ASJC Scopus subject areas

  • Geometry and Topology


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