Characterization of almost maximally almost-periodic groups

2009/03/08 by Gabriyelyan, S. S.
#22-xx #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.0903.1425

Abstract

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

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