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Maps Corresponding to the Subgroups \(\varGamma _0(N)\) of the Modular Group

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Abstract

The normalizer \(\varGamma _B(N)\) of \(\varGamma _0(N)\) in \(PSL(2,{\mathbb {R}})\) is the triangle group \((2,3,\infty )\) for \(N=2^\alpha 3^\beta \) where \(\alpha =0,2,4,6\); \(\beta =0,2\). In this paper we examine relationship between the normalizer and the regular maps for these values. We define a family of subgroups of the normalizer and then we study maps with triangular faces using these subgroups and calculating the associated arithmetic structure.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their helpful and constructive comments that greatly contributed to improving the final version of the paper. They would also like to thank the Editors for their generous comments and support during the review process.Finally, the first and second authors would like to thank TUBITAK (The Scientific and Technological Research Council of Turkey) for their financial supports during their doctorate studies.

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Authors and Affiliations

  1. Department of Mathematics, Karadeniz Technical University, 61080, Trabzon, Turkey

    Nazlı Yazıcı Gözütok, Uğur Gözütok & Bahadır Özgür Güler

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  1. Nazlı Yazıcı Gözütok
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  2. Uğur Gözütok
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  3. Bahadır Özgür Güler
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Correspondence to Nazlı Yazıcı Gözütok.

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Yazıcı Gözütok, N., Gözütok, U. & Güler, B.Ö. Maps Corresponding to the Subgroups \(\varGamma _0(N)\) of the Modular Group. Graphs and Combinatorics 35, 1695–1705 (2019). https://doi.org/10.1007/s00373-019-02080-9

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  • DOI: https://doi.org/10.1007/s00373-019-02080-9

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