1 9 Se p 19 98 Quasi - isometric rigidity for PSL 2 ( Z [ 1 p ] Jennifer Taback
نویسنده
چکیده
We prove that PSL2(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, PSL2(Z[ 1 p ]) and PSL2(Z[ 1 q ]) are not quasi-isometric unless p = q, and, independent of p, the quasi-isometry group of PSL2(Z[ 1 p ]) is PSL2(Q). In addition, we characterize PSL2(Z[ 1 p ]) uniquely among all finitely generated groups by its quasi-isometry type.
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