Index and Equality Conditions of the Subgroups $\Gamma_{0,n}(N)$ and $\Lambda_n(N)$

Authors : Aziz BÜYÜKKARAGÖZ, Erdal ÜNLÜYOL, Mehmet AKBAŞ

Pages : 60-64

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Publication Date : 2021-04-28

Article Type : Research Paper

Abstract :In this paper, we find conditions on the natural number $n$ that the subgroups $\Gamma_{0,n}insert ignore into journalissuearticles values(N);$ and $\Lambda_ninsert ignore into journalissuearticles values(N);$ of modular group are different. And then, by defining an $\Lambda_ninsert ignore into journalissuearticles values(N);$ invariant equivalence relation on the subset $\hat{\mathbb{Q}}_ninsert ignore into journalissuearticles values(N);$, we calculate the index formula for $\Gamma_{0,n}insert ignore into journalissuearticles values(N);$ in $\Lambda_ninsert ignore into journalissuearticles values(N);$.
Keywords : Congruence subgroup of modular group, transitivity, conjugateness, stabilizing, infinite cycle group, index formula