Minimally almost periodic group topology on countable torsion Abelian groups

2010/01/31 by Saak Gabriyelyan, Gabriyelyan, S. S.
Mathematics · #22A10 #43A40 #54H11 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1002.0141

openalex publication_date 2010/01/31 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

For any countable torsion subgroup H of an unbounded Abelian group G there is a complete Hausdorff group topology τ such that H is the von Neumann radical of (G,τ). 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.

Related

• Minimally almost periodic group topology on infinite countable Abelian groups: A solution to Comfort's question
• Which infinite abelian groups admit an almost maximally almost-periodic group topology?
• Final solution of Protasov-Comfort's problem on minimally almost periodic group topologies
• Characterization of almost maximally almost-periodic groups
• Locally Minimal Topological Groups 2