Abstract
It is proved that commensurable hyperbolic groups are bi-Lipschitz equivalent. Therefore, subgroups of finite index in an arbitrary hyperbolic group also share this property. In addition, it is shown that any two separated nets Γ1 and Γ2 in the hyperbolic space Hn of dimension n≥2 are bi-Lipschitz-equivalent. These results answer the questions posed in [1].
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