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arXiv · 2503.10321

The Profinite Rigidity of Free Metabelian Groups

Julian Wykowski
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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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Julian Wykowski. 2025-03-13. The Profinite Rigidity of Free Metabelian Groups. https://arxiv.org/abs/2503.10321

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