Locally compact Abelian groups with totally suitable sets

Abstract

We study the class S t of topological groups G that admit a totally suitable set, i.e., a relatively discrete subset S t Gnf1g such that S f1g is closed in G and N hSi is dense in N for each closed normal subgroup N of G. We resolve an open question from [10] by giving a complete description of the locally compact Abelian groups in S t . We also give a characterization of the groups of p-adic numbers in terms of totally suitable sets.