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Search: MSC category 22B05 ( General properties and structure of LCA groups )

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1. CMB 2011 (vol 56 pp. 213)

Tausk, Daniel V.
A Locally Compact Non Divisible Abelian Group Whose Character Group Is Torsion Free and Divisible
It was claimed by Halmos in 1944 that if $G$ is a Hausdorff locally compact topological abelian group and if the character group of $G$ is torsion free, then $G$ is divisible. We prove that such a claim is false by presenting a family of counterexamples. While other counterexamples are known, we also present a family of stronger counterexamples, showing that even if one assumes that the character group of $G$ is both torsion free and divisible, it does not follow that $G$ is divisible.


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