Unique product groups and congruence subgroups

Abstract

We prove that a uniform pro-p group with no nonabelian free subgroups has a normal series with torsion-free abelian factors. We discuss this in relation to unique product groups. We also consider generalizations of Hantzsche-Wendt groups.

8 pages, v2 minor changes, v3 minor changes, accepted by Journal of Algebra and its Applications