### abstract

- Let G be a lattice in PSL (2, C). The pro-normal topology on G is defined by taking all cosets of non-trivial 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 H< G is closed in the pro-normal topology. As a corollary we deduce that if M is a maximal subgroup of a lattice in PSL (2, C) then either M is finite index or M is not finitely generated. Subjects: Geometric Topology (math. GT); Group Theory (math. GR) Cite as: arXiv: math/0504441 [math. GT](or arXiv: math/0504441v1 [math. GT] for this version) Submission history From: Peter A. Storm [view email][v1] Thu, 21 Apr 2005 20: 59: 21 GMT (18kb)