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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221061A 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.General TopologyGroup Theory22A05 (Primary); 20K45, 54H11 (Secondary)Which infinite abelian groups admit an almost maximally almost-periodic group topology?text