Identifying congruence subgroups of the modular group

Author:

Hsu Tim

Abstract

We exhibit a simple test (Theorem 2.4) for determining if a given (classical) modular subgroup is a congruence subgroup, and give a detailed description of its implementation (Theorem 3.1). In an appendix, we also describe a more “invariant” and arithmetic congruence test.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference13 articles.

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3. The Schur multiplicator of 𝑆𝐿(2,𝑍/𝑚𝑍) and the congruence subgroup property;Beyl, F. Rudolf;Math. Z.,1986

4. On the construction of noncongruence subgroups;Britto, Juliet;Acta Arith.,1977

5. Special polygons for subgroups of the modular group and applications;Chan, Shih-Ping;Internat. J. Math.,1993

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