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The number of subgroups of given index in the modular group*

Published online by Cambridge University Press:  14 February 2012

W. W. Stothers
W. W. Stothers
Affiliation:
Department of Mathematics, University of Glasgow
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Synopsis

A new formula is obtained for the number of subgroups of given index in the modular group. The formula is used to prove a recent conjecture on the parity of the number of subgroups.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 78 , Issue 1-2 , 1977 , pp. 105 - 112
Copyright
Copyright © Royal Society of Edinburgh 1977

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References

1Dey, I. M. S.Schreier systems in free products. Proc. Glasgow Math. Assoc. 7 (1965), 61–79.CrossRefGoogle Scholar
2Dickson, L. E.History of the theory of numbers, I (New York: Chelsea, 1919).Google Scholar
3Millington, M. H.Subgroups of the classical modular group. J. London Math. Soc. 1 (1970), 351–357.Google Scholar
4Newman, M.Asymptotic formulas related to free products of cyclic groups. Math. Comp, 30 (1976), 838–846.CrossRefGoogle Scholar
5Stothers, W. W.Subgroups of the modular group. Proc. Cambridge Philos. Soc. 75 (1974), 139–153.CrossRefGoogle Scholar
6Stothers, W. W. On some discrete triangle groups (Cambridge Univ. Ph.D. Thesis, 1971).Google Scholar