Finitely generated subgroups of lattices in PSL₂ℂ

Let G be a lattice in PSL₂(C). The pro-normal topology on G is defined by taking all cosets of nontrivial normal subgroups as a basis. This topology is finer than the pro-finite topology, but it is not discrete. We prove that every finitely generated subgroup δ < G is closed in the pro-normal topology. As a corollary we deduce that if H is a maximal subgroup of a lattice in PSL₂(C), then either H is of finite index or H is not finitely generated.