  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.
