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

Nicolas Mayorga Uruburu; Ariel Pacetti; Leandro Vendramin

doi:10.1142/S0219498825502159

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

Nicolas Mayorga Uruburu, Ariel Pacetti, Leandro Vendramin

Research output: Contribution to journal › Article › peer-review

Abstract

We present a method to compute finite index subgroups of PSL₂(ℤ). Our strategy follows Kulkarni’s ideas, the main contribution being a recursive method to compute bivalent trees as well as their automorphism groups. 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.

Original language	English
Article number	2550215
Number of pages	42
Journal	Journal of Algebra and Its Applications
Volume	24
Issue number	9
DOIs	https://doi.org/10.1142/S0219498825502159 https://doi.org/10.48550/arXiv.2307.01826
Publication status	Published - 2025

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© 2025 World Scientific Publishing Company.

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abstract = "We present a method to compute finite index subgroups of PSL2(ℤ). Our strategy follows Kulkarni{\textquoteright}s ideas, the main contribution being a recursive method to compute bivalent trees as well as their automorphism groups. 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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AB - We present a method to compute finite index subgroups of PSL2(ℤ). Our strategy follows Kulkarni’s ideas, the main contribution being a recursive method to compute bivalent trees as well as their automorphism groups. 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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On computing finite index subgroups of PSL(2,Z)

Abstract

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Subgroups of SL(2,Z)

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

Abstract

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Subgroups of SL(2,Z)

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