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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Normalizers of the congruence subgroups
of the Hecke group $G_{5}$ II


Authors: Mong-Lung Lang and Ser-Peow Tan
Journal: Proc. Amer. Math. Soc. 128 (2000), 2271-2280
MSC (1991): Primary 11F06
Published electronically: February 25, 2000
MathSciNet review: 1712893
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Abstract: Let $\lambda = 2\cos(\pi /5)$. Let $(\tau )$ be an ideal of $\mathbb{Z}[\lambda ]$ and let $(\tau _0)$ be the maximal ideal of $\mathbb{Z}[\lambda]$ such that $(\tau _0^2)\subseteq(\tau)$. Then $N(G_0(\tau))\le G_0(\tau _0)$. In particular, if $\tau $ is square free, then $G_{0}(\tau )$ is self-normalized in $PSL_{2}(\mathbb{R})$.


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Additional Information

Mong-Lung Lang
Affiliation: Department of Mathematics, National University of Singapore, Singapore 119260, Republic of Singapore
Email: matlml@math.nus.edu.sg

Ser-Peow Tan
Affiliation: Department of Mathematics, National University of Singapore, Singapore 119260, Republic of Singapore
Email: mattansp@nus.edu.sg

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05677-X
PII: S 0002-9939(00)05677-X
Keywords: Congruence subgroups, Hecke groups
Received by editor(s): September 25, 1998
Published electronically: February 25, 2000
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 2000 American Mathematical Society