Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-23T04:25:15.043Z Has data issue: false hasContentIssue false

Subgroups of infinite index in the modular group

Published online by Cambridge University Press:  18 May 2009

W. W. Stothers
Affiliation:
University of Glasgow, Glasgow G12 8QW
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The modular group Г is the group of integral bilinear transformations of the extended complex plane which preserve the upper half-plane. It has the presentation 〈x, y:x2 = y3 = 1〉, and the generators can be chosen so that u = xy maps z to z + 1.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1978

References

REFERENCES

1.Harary, F., Graph theory (Addison-Wesley, 1969).CrossRefGoogle Scholar
2.Lehner, J., Discontinuous groups and automorphic functions (Amer. Math. Soc, 1964).CrossRefGoogle Scholar
3.Mason, A. W., On a theorem by Leon Greenberg, Proc. Amer. Math. Soc. 23 (1969), 1823.Google Scholar
4.Millington, M. H., On cycloidal subgroups of the modular group, Proc. London Math. Soc. (3), 19 (1969), 164176.CrossRefGoogle Scholar
5.Millington, M. H., Subgroups of the classical modular group, J. London Math Soc. (2), 1 (1969), 351357.Google Scholar
6.Stothers, W. W., Subgroups of the modular group, Proc. Cambridge Philos. Soc. 75 (1974), 139153.Google Scholar
7.Stothers, W. W., Impossible specifications for the modular group, Manuscripta Math. 13 (1974), 415428.Google Scholar
8.Tretkoff, C., Nonparabolic subgroups of the modular group, Glasgow Math. J. 16 (1975), 91102.Google Scholar