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math.GR2025
The Profinite Rigidity of Torsion-Free Lamplighter Groups
Nikolay Nikolov, Julian Wykowski
We prove that the torsion-free lamplighter group of any rank is profinitely rigid in the absolute sense: the finite quotients of…
math.GR2025
The Profinite Rigidity of Free Metabelian Groups
Julian Wykowski
We prove that finitely generated free metabelian groups are profinitely rigid in the absolute sense: they are distinguished by their finite quotients among all finitely gener…
math.GR2025
Profinite Rigidity over Noetherian Domains
Julian Wykowski
We initiate the study of profinite rigidity for modules over a Noetherian domain: to what extent are these objects determined by their finite images? We establish foundational stat…