Minimally almost periodic group topology on infinite countable Abelian groups: A solution to Comfort's question

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Abstract

For any countable subgroup $H$ of an unbounded Abelian group $G$ there is a complete Hausdorff group topology $\tau$ such that $H$ is the von Neumann radical of $(G,\tau)$. In particular, we obtain the positive answer to Comfort's question: any unbounded countable Abelian group admits a complete Hausdorff minimally almost periodic (MinAP) group topology. A bounded infinite Abelian group admits a MinAP group topology if and only if all its leading Ulm-Kaplansky invariants are infinite. If, in addition, $G$ is countably infinite, a MinAP group topology can be chosen to be complete.
Original languageEnglish GB
StatePublished - 2010

Publication series

NameArxiv preprint

Keywords

  • math.GR
  • math.GN
  • 22A10, 43A40, 54H11

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