Minimally almost periodic group topology on countable torsion Abelian groups

Details Minimally almost periodic group topology on countable torsion Abelian groups Minimally almost periodic group topology on countable torsion Abelian groups

2010-01-31

arxiv.org/abs/1002.0141v2

Mathematics

Group Theory

Scientific paper

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.

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