  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.
