2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/227497Let k be a local field and G the set of k-points of a connected semisimple algebraic k-group of rank one. We describe all torsion-free discrete subgroups of G\times G acting properly discontinuously on G by left and right multiplication. To this end, we prove a general result on the Cartan projection of discrete groups acting properly discontinuously on corank-one reductive homogeneous spaces over k.17 pagesGroup Theory20G25; 22E40; 57S30text