Congruence Subgroups Associated to the Monster

Abstract

Let Δ = {G : g(G) = 0,Γ₀(m) ≤ G ≤ N(Γ₀(m)) for some m}, where N(Γ₀(m)) is the normaliser of Γ₀(m) in PSL ₂(R) and g(G) is the genus of H*/G. In this article, we determine all the m. Further, for each m, we list all the intermediate groups G of Γ₀(m) ≤ N(Γ₀(m)) such that g(G) = 0. All the intermediate groups of width 1 at ∞ are also listed in a separatetable (see www.rnath.nus.edu.sg/e-matlml/).

Keywords:

• Congruence subgroups
• genus
• Monster simple group