The Profinite Rigidity of Free Metabelian Groups

2025/03/13 by Wykowski, Julian · 1 citation
#13C10 #13C60 (Secondary) #20E18 #20F16 (Primary) 13D07 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2503.10321

Abstract

We prove that finitely generated free metabelian groups Ψ_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.

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