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A Locally Compact Non Divisible Abelian Group Whose Character Group Is Torsion Free and Divisible

Published online by Cambridge University Press:  20 November 2018

Daniel V. Tausk
Daniel V. Tausk*
Affiliation:
Departamento de Matemática, Universidade de São Paulo, Brazil e-mail: tausk@ime.usp.br
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Abstract

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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.

Keywords

22B05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 1 , 01 March 2013 , pp. 213 - 217
Copyright
Copyright © Canadian Mathematical Society 2013

References

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