English

On computing finite index subgroups of PSL(2,Z)

Number Theory 2025-05-13 v1 Group Theory

Abstract

We present a method to compute finite index subgroups of PSL2(Z)PSL_2(\mathbb{Z}). Our strategy follows Kulkarni's ideas, the main contribution being a recursive method to compute bivalent trees and their automorphism group. As a concrete application, we compute all subgroups of index up to 20. We then use this database to produce tables with several arithmetical properties.

Keywords

Cite

@article{arxiv.2307.01826,
  title  = {On computing finite index subgroups of PSL(2,Z)},
  author = {Nicolás Mayorga Uruburu and Ariel Pacetti and Leandro Vendramin},
  journal= {arXiv preprint arXiv:2307.01826},
  year   = {2025}
}

Comments

27 pages, several figures