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The Profinite Rigidity of Free Metabelian Groups (2503.10321v2)
Published 13 Mar 2025 in math.GR
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.
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