ON SUBORBITAL GRAPH FOR THE CONGRUENCE SUBGROUP $\Gamma_{0,n}(N)$
Zeynep Şanlı, Mehmet Akbaş · Far East Journal of Mathematical Sciences (FJMS) · 2020
In this paper, we calculate the index of $\Gamma_{0,n}(N)$ in $\Gamma_0(N), n|N$ by using the imprimitive action of the transitive permutation group $(\Gamma_0(N),\mathbf{\hat{Q}}(N))$. Then some combinatorial properties are given when $n|24$ and $n mid 24$. Finally, we investigate suborbital graphs formed by the action of $\Gamma_0(N)$ on $\mathbf{\hat{Q}}(N)$, give the edge conditions of the graph, and show that $F_{u,N}$ contains no triangle.