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Quasi-isometric rigidity for PSL(2,Z[1/p])

Jennifer Taback
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Abstract

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.

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Jennifer Taback. 1998-09-19. Quasi-isometric rigidity for PSL(2,Z[1/p]). https://arxiv.org/abs/math/9809108

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