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 Γ< G any lattice, then up to a small perturbation and passing to a finite index subgroup, F is a subgroup of Γ. If G/Γis noncompact then we require additional hypotheses that include G=SO(n,1).

This version corrects a few typos. Version 4 is a major rewrite over version 3

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