Finitely generated subgroups of lattices in PSL2

Yair Glasner, Juan Souto, Peter Storm

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)2667-2676
Number of pages10
JournalProceedings of the American Mathematical Society
Volume138
Issue number8
DOIs
StatePublished - 1 Aug 2010

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