## Experimental Mathematics

- Experiment. Math.
- Volume 13, Issue 3 (2004), 343-360.

### Congruence Subgroups Associated to the Monster

Kok Seng Chua and Mong Lung Lang

#### Abstract

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 www.math.nus.edu.sg/$\sim$matlml/).

#### Article information

**Source**

Experiment. Math., Volume 13, Issue 3 (2004), 343-360.

**Dates**

First available in Project Euclid: 22 December 2004

**Permanent link to this document**

https://projecteuclid.org/euclid.em/1103749842

**Mathematical Reviews number (MathSciNet)**

MR2103332

**Zentralblatt MATH identifier**

1099.11021

**Subjects**

Primary: 20H05: Unimodular groups, congruence subgroups [See also 11F06, 19B37, 22E40, 51F20]

Secondary: 11F06: Structure of modular groups and generalizations; arithmetic groups [See also 20H05, 20H10, 22E40]

**Keywords**

Congruence subgroups genus Monster simple group

#### Citation

Chua, Kok Seng; Lang, Mong Lung. Congruence Subgroups Associated to the Monster. Experiment. Math. 13 (2004), no. 3, 343--360. https://projecteuclid.org/euclid.em/1103749842