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Subgroups of the modular group

Published online by Cambridge University Press:  24 October 2008

W. W. Stothers
W. W. Stothers
Affiliation:
Department of Mathematics, University Gardens, Glasgow G12 8QW
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Extract

The modular group, Γ, is the group of linear fractional transformations with integral coefficients and determinant 1. The group is generated by the transformations

which have orders 2 and 3 respectively. The transformation

is of infinite order. Abstractly, the group can be viewed as the free product of cyclic groups of order 2 and 3.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 75 , Issue 2 , March 1974 , pp. 139 - 153
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

(1)Millington, M. H.On cycloidal subgroups of the modular group. Proc. London Math. Soc. (3), 19 (1969), 164–176.CrossRefGoogle Scholar
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(3)Atkin, A. O. L. and Swinnerton-Dyer, H. P. F.Modular forms on non-congruence subgroups. A.M.S. Symposium on Combinatorics, Los Angeles.Google Scholar
(4)Singermann, D.Subgroups of Fuchsian groups and finite permutation groups. Bull. London Math. Soc. 2 (1970), 319–323.CrossRefGoogle Scholar