# Minimally almost periodic group topology on countable torsion Abelian groups

Research output: Working paper/PreprintPreprint

## 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 language English GB Published - 2010

### Publication series

Name Arxiv preprint

## Keywords

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

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