Normalizers of the congruence subgroups of the Hecke group II

Lang, Mong-Lung; Tan, Ser-Peow

doi:10.1090/S0002-9939-00-05677-X

Normalizers of the congruence subgroups of the Hecke group II
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by Mong-Lung Lang and Ser-Peow Tan PDF

Proc. Amer. Math. Soc. 128 (2000), 2271-2280 Request permission

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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