%0 Journal Article
%T Quasi-isometric rigidity for PSL(2,Z[1/p])
%A Jennifer Taback
%J Mathematics
%D 1998
%I arXiv
%X We prove that PSL(2,Z[1/p]) gives the first example of groups which are not quasi-isometric to each other but have the same quasi-isometry group. Namely, PSL(2,Z[1/p]) and PSL(2,Z[1/q]) are not quasi-isometric unless p=q, and, independent of p, the quasi-isometry group of PSL(2,Z[1/p]) is PSL(2,Q). In addition, we characterize PSL(2,Z[1/p]) uniquely among all finitely generated groups by its quasi-isometry type.
%U http://arxiv.org/abs/math/9809108v1