The Profinite Rigidity of Torsion-Free Lamplighter Groups

Nikolay Nikolov, Julian Wykowski

We prove that the torsion-free lamplighter group $\hat{I}“={\mathbb{Z}}^n\wr \mathbb{Z}$ of any rank $n\in \mathbb{N}$ is profinitely rigid in the absolute sense: the finite quotients o…