The Profinite Rigidity of Free Metabelian Groups

Abstract

We prove that finitely generated free metabelian groups ${\Psi }_n$ are profinitely rigid in the absolute sense: they are distinguished by their finite quotients among all finitely generated residually finite groups. The proof is based on a previous result of the author governing profinite rigidity for modules over Noetherian domains, as well as a homological characterisation of free metabelian groups due to Groves--Miller.

arXiv comment13 pages, comments welcome. V2 is a minor update featuring more detailed explanations and the resolution of some typos