2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79403We construct examples of groups showing that virtual solvability and the property of being virtually torsion-free are not preserved by bi-Lipschitz maps and hence by quasi-isometries.Group Theory20F65Instability of the virtual solvability and the property of being virtually torsion-free for quasi-isometric groupstext