A Nunke type classification in the locally compact setting

Samuel M. Corson; Olga Varghese

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arXiv · 1912.11867

A Nunke type classification in the locally compact setting

Samuel M. Corson·Olga Varghese

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Abstract

In this short note we prove that a group G is lcH-slender -- that is, every abstract group homomorphism from a locally compact Hausdorff topological group to G has an open kernel -- if and only if G is torsion-free and does not include Q or the p-adic integers Zp for any prime p. This mirrors a classical characterization given by Nunke for slender abelian groups.

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Samuel M. Corson, Olga Varghese. 2019-12-26. A Nunke type classification in the locally compact setting. https://arxiv.org/abs/1912.11867

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