2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159957Suppose $G$ is a countable, not necessarily finitely generated, group. We show $G$ admits a proper, left-invariant metric $d_G$ such that the Assouad-Nagata dimension of $(G,d_G)$ is infinite, provided the center of $G$ is not locally finite. As a corollary we solve two problems of A.Dranishnikov.9 pagesMetric GeometryGroup TheoryGeometric Topology54F45 (Primary); 55M10, 54C65 (Secondary)text