Free subgroups with torsion quotients and profinite subgroups with torus quotients

Abstract

Here “group” means abelian group. Compact connected groups contain $\delta$-subgroups, that is, compact totally disconnected subgroups with torus quotients, which are essential ingredients in the important Resolution Theorem, a description of compact groups. Dually, full free subgroups of discrete torsion-free groups of finite rank are studied in order to obtain a comprehensive picture of the abundance of $\delta$-subgroups of a protorus. Associated concepts are also considered.