Nikolay K. Nikolov

The profinite rigidity of torsion-free lamplighter groups

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...