S.S. Gabriyelyan
Minimally almost periodic group topology on infinite countable Abelian groups. A solution to Comfort's question.
Втр, 02/09/2010 - 16:01 — SomNambulAuthors: S.S. Gabriyelyan
Subjects: Group Theory
AbstractFor any countable subgroup $H$ of an unbounded Abelian group $G$ there is a
complete Hausdorff group topology $\tau$ such that $H$ is the von Neumann
radical of $(G,\tau)$. In particular, we obtain the positive answer to
Comfort's question: any unbounded countable Abelian group admits a complete
Hausdorff minimally almost periodic group topology.Minimally almost periodic group topology on countable torsion Abelian groups.
Втр, 02/02/2010 - 16:01 — SomNambulAuthors: S.S. Gabriyelyan
Subjects: Group Theory
AbstractFor any countable torsion subgroup $H$ of an unbounded Abelian group $G$
there is a complete Hausdorff group topology $\tau$ such that $H$ is the von
Neumann radical of $(G,\tau)$. 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.
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