Bilipschitz versus quasi-isometric equivalence for higher rank lamplighter groups

Abstract

We describe a family of finitely presented groups which are quasi-isometric but not bilipschitz equivalent. The first such examples were described by the first author and are the lamplighter groups $F\wr \mathbb{Z}$ where $F$ is a finite group; these groups are finitely generated but not finitely presented. The examples presented in this paper are higher rank generalizations of these lamplighter groups and include groups that are of type $F_n$ for any $n$.

References in corpus (1)

• Lamplighters, Metabelian Groups, and Horocyclic Products of Trees