2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70760Whyte showed that any quasi-isometry between non-amenable groups is a bounded distance from a bijection. In contrast this paper shows that for amenable groups, inclusion of a proper subgroup of finite index is never a bounded distance from a bijection.8 pages, 1 figureGroup Theory20F65text