Open Access
2004 Congruence Subgroups Associated to the Monster
Kok Seng Chua, Mong Lung Lang
Experiment. Math. 13(3): 343-360 (2004).


Let {\small $\Delta = \{ G: g(G) =0, \Gamma_0(m) \le G \le N(\Gamma_0(m))$ $\mbox{ for some }m\},$} where {\small $N(\Gamma_0(m))$} is the normaliser of {\small $\Gamma_0(m)$} in {\small $PSL_2(\Bbb R)$} and {\small $g(G)$} is the genus of {\small $\Bbb H^*/G$}. In this article, we determine all the {\small $m$}. Further, for each {\small $m$}, we list all the intermediate groups {\small $G$} of {\small $\Gamma_0(m) \le N(\Gamma_0(m))$} such that {\small $ g(G) =0$}. All the intermediate groups of width 1 at {\small $\infty$} are also listed in a separate table (see$\sim$matlml/).


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Kok Seng Chua. Mong Lung Lang. "Congruence Subgroups Associated to the Monster." Experiment. Math. 13 (3) 343 - 360, 2004.


Published: 2004
First available in Project Euclid: 22 December 2004

zbMATH: 1099.11021
MathSciNet: MR2103332

Primary: 20H05
Secondary: 11F06

Keywords: congruence subgroups , genus , Monster simple group

Rights: Copyright © 2004 A K Peters, Ltd.

Vol.13 • No. 3 • 2004
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