A Nunke type classification in the locally compact setting
Group Theory
2020-10-07 v1
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.
Cite
@article{arxiv.1912.11867,
title = {A Nunke type classification in the locally compact setting},
author = {Samuel M. Corson and Olga Varghese},
journal= {arXiv preprint arXiv:1912.11867},
year = {2020}
}