Abstract
We give an explicit formula for the number of subgroups of the modular group of a given index that are genus zero and torsion-free, and a formula for their conjugacy classes. We do so by exhibiting a correspondence between these groups and the trivalent maps on a sphere. We focus on the particular case of the subgroups of index 18 which have some interesting geometric properties.
Citation
Abdellah Sebbar. Khalil Besrour. "Modular groups and planar maps." Rocky Mountain J. Math. 51 (5) 1847 - 1863, October 2021. https://doi.org/10.1216/rmj.2021.51.1847
Information