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 : 19 | Download : 6

Publication Date : 2022-06-01

Article Type : Research Paper

Abstract :In this paper, we investigate suborbital graphs $G_{u,n}$ of the normalizer $\Gamma_Binsert ignore into journalissuearticles values(N);$ of $\Gamma_0insert ignore into journalissuearticles values(N);$ in $PSLinsert ignore into journalissuearticles values(2,\mathbb{R});$ 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 $\Gamma _Binsert ignore into journalissuearticles values(N);$ on $\widehat{\mathbb{Q}}$ using the group $H_Binsert ignore into journalissuearticles values(N);$ and then we obtain some properties of the graphs arising from this action.
Keywords : normalizer, suborbital graph, hexagon