2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70328Let k be a local field, and G a linear group over k. We prove that either G contains a relatively open solvable subgroup, or it contains a relatively dense free subgroup. This result has applications in dynamics, Riemannian foliations and profinite groups.43 pagesGroup Theory20G25text