2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/227568We show that two uniform lattices of a regular right-angled Fuchsian building are commensurable, provided the chamber is a polygon with at least six edges. We show that in an arbitrary Gromov-hyperbolic regular right-angled building associated to a graph product of finite groups, a uniform lattice is commensurable with the graph product provided all of its quasiconvex subgroups are separable. We obtain a similar result for uniform lattices of the Davis complex of Gromov-hyperbolic two-dimensional Coxeter groups. We also prove that every extension of a uniform lattice of a CAT(0) square complex by a finite group is virtually trivial, provided each quasiconvex subgroup of the lattice is separable.This is the version published by Algebraic & Geometric Topology on 9 August 2006Group TheoryGeometric Topology20F55, 20F65, 20F67, 20E22, 20E26, 20J06, 51E24text