Finitely generated subgroups of lattices in PSL(2,C)
Yair Glasner, Juan Souto, Peter Storm
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.
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