Minimally almost periodic group topology on countable torsion Abelian groups

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.

References in corpus (2)

• Almost maximally almost-periodic group topologies determined by T-sequences
• Which infinite abelian groups admit an almost maximally almost-periodic group topology?