The profinite rigidity of torsion-free lamplighter groups
Abstract
Abstract We prove that the torsion-free lamplighter group $$\Gamma = \mathbb {Z}^n \wr \mathbb {Z}$$ Γ = Z n ≀ Z of any rank $$n \in \mathbb {N}$$ n ∈ N is profinitely rigid in the absolute sense: the finite quotients of $$\Gamma $$ Γ determine its isomorphism type uniquely among all finitely generated residually finite groups. The proof combines the theory of profinite rigidity for modules over Noetherian domains with an analysis of the algebraic properties of the lower central series of groups with the same profinite completion as $$\Gamma $$ Γ .
Fields of Study & Subjects
Geometric and Algebraic Topology
Rings
Modules
and Algebras
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Mathematische Annalen
- Volume
- 396
- Issue
- 1
- Pages
- 17–17
- Publication date
- 20 August 2026
- Language
- EN