Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-15T08:16:57.943Z Has data issue: false hasContentIssue false
  • English
  • Français

The normalizer of Γ0(N) in PSL(2, ℝ)

Published online by Cambridge University Press:  18 May 2009

M. Akbas  and
D. Singerman
M. Akbas
Affiliation:
Faculty of Mathematical Studies, The University, Southampton.
D. Singerman
Affiliation:
Faculty of Mathematical Studies, The University, Southampton.
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.

Let Γ denote the modular group, consisting of the Möbius transformations

As usual we denote the above transformation by the matrix remembering that V and – V represent the same transformation. If N is a positive integer we let Γ0(N) denote the transformations for which c ≡ 0 mod N. Then Γ0(N) is a subgroup of index

the product being taken over all prime divisors of N.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 32 , Issue 3 , September 1990 , pp. 317 - 327
Copyright
Copyright © Glasgow Mathematical Journal Trust 1990

References

REFERENCES

1.Atkin, A. O. L. and Lehner, J., Hecke operators on Γ0(m). Math. Ann. 185 (1970) 134–160.CrossRefGoogle Scholar
2.Conway, C. and Norton, S., Monstrous moonshine. Bull. London Math. Soc. 11 (1979) 308–339.CrossRefGoogle Scholar
3.Coxeter, H. M. S., The abstract group G m.n.p. Trans. Amer. Soc. 45 (1939) 73–150.Google Scholar
4.Johnson, D. L., Presentation of groups. London Math. Soc. Lecture Notes No. 22, (Cambridge University Press, 1976).Google Scholar
5.Lehner, J. and Newman, M., Weierstrass points on Γ0(N). Ann. of Math. 79 (1964) 360–368.CrossRefGoogle Scholar
6.Maclachlan, C., Groups of units of zero ternary quadratic forms. Proc. Roy. Soc. Edinburgh Sect. A, 88 (1981) 141–157.CrossRefGoogle Scholar
7.Ogg, A. P., Modular functions in Proceedings Santa Cruz Conference on Finite Groups, Proc. Symp. Pure Math. 37 (A.M.S. 1980).Google Scholar
8.Ogg, A. P., “Uber die Automorphismengruppe von X 0(N)”. Math. Ann. 228 (1977) 279–292.CrossRefGoogle Scholar
9.Schoeneberg, B., Elliptic modular functions. (Springer-Verlag, 1974).CrossRefGoogle Scholar
10.Sherk, F. A., The regular maps on a surface of genus three. Canad. J. Math. 11 (1959), 452–480.CrossRefGoogle Scholar
11.Singerman, D., Symmetries of Riemann surfaces with large automorphism group. Math. Ann. 210 (1974), 17–32.CrossRefGoogle Scholar
12.Zomorrodian, R., Nilpotent automorphism groups of Riemann surfaces, Trans. Amer. Math. Soc. 288 (1985) 241–255.Google Scholar