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Journals / Hacettepe Journal of Mathematics and Statistics / 2022 / Cilt: 51 - Sayı: 3

Hexagonal cell graphs of the normalizer with signature $(2, 6, \infty)$

Nazlı YAZICI GÖZÜTOK
Bahadır Özgür GÜLER
Pages
666–679
Publication Date
2022-06-01
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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 $\beta =1,3$.
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Key Findings & Data:In each of these cases, the normalizer becomes a triangle group and the graph arising from the action of the normalizer contains hexagonal circuits.
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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:normalizer · suborbital graph · hexagon

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.

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Cite This Article

GÖZÜTOK, N. Y., GÜLER, B. Ö. (2022). Hexagonal cell graphs of the normalizer with signature $(2, 6, \infty)$. Hacettepe Journal of Mathematics and Statistics, Cilt: 51 - Sayı: 3, 666–679. https://ajindex.com/articles/669192

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