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For any countable subgroup $H$ of an unbounded Abelian group $G$ there is acomplete Hausdorff group topology $\tau$ such that $H$ is the von Neumannradical of $(G,\tau)$. In particular, we obtain the positive answer toComfort's question: any unbounded countable Abelian group admits a completeHausdorff minimally almost periodic (MinAP) group topology. A bounded infiniteAbelian group admits a MinAP group topology if and only if all its leadingUlm-Kaplansky invariants are infinite. If, in addition, $G$ is countablyinfinite, a MinAP group topology can be chosen to be complete.

Minimally almost periodic group topology on infinite countable Abelian groups: A solution to Comfort's question