- Hacettepe Journal of Mathematics and Statistics
- Vol: 51 Issue: 3
- Hexagonal cell graphs of the normalizer with signature $(2, 6, \infty)$
Hexagonal cell graphs of the normalizer with signature $(2, 6, \infty)$
Authors : Nazlı Yazici Gözütok, Bahadır Özgür Güler
Pages : 666-679
Doi:10.15672/hujms.824436
View : 13 | Download : 4
Publication Date : 2022-06-01
Article Type : Research
Abstract :In this paper, we investigate suborbital graphs $G_{u,n}$ of the normalizer $\Gamma_B(N)$ of $\Gamma_0(N)$ in $PSL(2,\mathbb{R})$ for $N= 2^\alpha 3^\beta$, where $\alpha=0,2,4,6$ and $\beta =1,3$. In each of these cases, the normalizer becomes a triangle group and the graph arising from the action of the normalizer contains hexagonal circuits. In order to obtain graphs, we first define an imprimitive action of $\Gamma _B(N)$ on $\widehat{\mathbb{Q}}$ using the group $H_B(N)$ and then we obtain some properties of the graphs arising from this action.Keywords : normalizer, suborbital graph, hexagon