Which infinite abelian groups admit an almost maximally almost-periodic group topology?

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A topological group G is said to be almost maximally almost-periodic if its von Neumann radical is non-trivial, but finite. In this paper, we prove that every abelian group with an infinite torsion subgroup admits a (Hausdorff) almost maximally almost-periodic group topology. Some open problems are also formulated.

💡 Research Summary

The paper investigates the existence of “almost maximally almost‑periodic” (AMAP) group topologies on infinite abelian groups. A topological group (G) is called AMAP if its von Neumann radical
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Which infinite abelian groups admit an almost maximally almost-periodic group topology?

💡 Research Summary

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