Finitely generated subgroups of lattices in PSL(2,C)
Geometric Topology
2007-05-23 v1 Group Theory
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.
Cite
@article{arxiv.math/0504441,
title = {Finitely generated subgroups of lattices in PSL(2,C)},
author = {Yair Glasner and Juan Souto and Peter Storm},
journal= {arXiv preprint arXiv:math/0504441},
year = {2007}
}