Minimally almost periodic group topology on countable torsion Abelian groups

Research output: Working paper/PreprintPreprint

15 Downloads (Pure)

Abstract

For any countable torsion 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, any unbounded torsion countable Abelian group admits a complete Hausdorff minimally almost periodic (MinAP) group topology. If $G$ is a bounded torsion countably infinite Abelian group, then it admits a MinAP group topology if and only if all its leading Ulm-Kaplansky invariants are infinite. In such a case, 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

Fingerprint

Dive into the research topics of 'Minimally almost periodic group topology on countable torsion Abelian groups'. Together they form a unique fingerprint.

Cite this