- Konuralp Journal of Mathematics
- Vol: 9 Issue: 1
- Index and Equality Conditions of the Subgroups $\Gamma_{0,n}(N)$ and $\Lambda_n(N)$
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
Abstract :In this paper, we find conditions on the natural number $n$ that the subgroups $\Gamma_{0,n}(N)$ and $\Lambda_n(N)$ of modular group are different. And then, by defining an $\Lambda_n(N)$ invariant equivalence relation on the subset $\hat{\mathbb{Q}}_n(N)$, we calculate the index formula for $\Gamma_{0,n}(N)$ in $\Lambda_n(N)$.Keywords : Congruence subgroup of modular group, transitivity, conjugateness, stabilizing, infinite cycle group, index formula