Characterization of almost maximally almost-periodic groups

Details Characterization of almost maximally almost-periodic groups Characterization of almost maximally almost-periodic groups

2009-03-08

arxiv.org/abs/0903.1425v1

Mathematics

General Topology

Scientific paper

Let $G$ be an abelian group. We prove that a group $G$ admits a Hausdorff group topology $\tau$ such that the von Neumann radical $\mathbf{n}(G, \tau)$ of $(G, \tau)$ is non-trivial and finite iff $G$ has a non-trivial finite subgroup. If $G$ is a topological group, then $\mathbf{n} (\mathbf{n} (G)) \not= \mathbf{n} (G)$ if and only if $\mathbf{n} (G)$ is not dually embedded. In particular, $\mathbf{n} (\mathbf{n} (\mathbb{Z},\tau)) = \mathbf{n} (\mathbb{Z},\tau)$ for any Hausdorff group topology $\tau$ on $\mathbb{Z}$.

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