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Commutators, commensurators, and PSL2(Z)
Journal of Topology  (IF1.582),  Pub Date : 2021-07-09, DOI: 10.1112/topo.12200
Thomas Koberda, Mahan Mj

Let H < PSL 2 ( Z ) be a finite index normal subgroup which is contained in a principal congruence subgroup, and let Φ ( H ) H denote a term of the lower central series or the derived series of H . In this paper, we prove that the commensurator of Φ ( H ) in PSL 2 ( R ) is discrete. We thus obtain a natural family of thin subgroups of PSL 2 ( R ) whose commensurators are discrete, establishing some cases of a conjecture of Shalom.