Free groups in lattices

Abstract

Let $G$ be any locally compact unimodular metrizable group. The main result of this paper, roughly stated, is that if $F<G$ is any finitely generated free group and $\Gamma <G$ any lattice, then up to a small perturbation and passing to a finite index subgroup, $F$ is a subgroup of $\Gamma$. If $G∕\Gamma$ is noncompact then we require additional hypotheses that include $G=SO\left(n,1\right)$.