Finitely generated subgroups as von Neumann radicals of an Abelian group

Author S. S. Gabriyelyan
Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva, Israel

Abstract Let G be an infinite Abelian group. We give a complete characterization of those finitely generated subgroups of G which are the von Neumann radicals for some Hausdorff group topologies on G. It is proved that every infinite finitely generated Abelian group admits a complete Hausdorff minimally almost periodic group topology. The latter result resolves a particular case of Comfort’s problem.
Keywords characterized group; T-sequence; von Neumann radical; finitely generated subgroup
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Pages 124-138
Volume 38
Issue 2
Year 2012
Journal Matematychni Studii
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