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arXiv · 2307.01826

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

Nicolás Mayorga Uruburu·Ariel Pacetti·Leandro Vendramin
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Abstract

We present a method to compute finite index subgroups of $PSL_2(\mathbb{Z})$. 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.

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Nicolás Mayorga Uruburu, Ariel Pacetti, Leandro Vendramin. 2023-07-04. On computing finite index subgroups of PSL(2,Z). https://doi.org/10.1142/s0219498825502159

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