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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Finally, The number of boundary components in the signature of some groups $\hat{\Gamma}_{0,p}(p)$ and $\hat{\Gamma}_{0,p}(p^2), p$ is a prime number, and the number of link periods were found.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we established the group $\hat{\Gamma}_{0,n}(N)$ by group $\Gamma_{0,n}(N)$ extending with reflection.
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Key Findings & Data:Then, we obtain boundary components in signature of the group and we get some calculation for link periods $2, 3, \infty$.
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Conclusion & Impact:Finally, The number of boundary components in the signature of some groups $\hat{\Gamma}_{0,p}(p)$ and $\hat{\Gamma}_{0,p}(p^2), p$ is a prime number, and the number of link periods were found.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Signature · Boundary component · Extended Modular Group
Abstract
In this paper, we established the group $\hat{\Gamma}_{0,n}(N)$ by group $\Gamma_{0,n}(N)$ extending with reflection. Then, we obtain boundary components in signature of the group and we get some calculation for link periods $2, 3, \infty$. And then, we constitute chain of reflections with fixed points via extended Hoore-Uzzell Theorem in the group. Finally, The number of boundary components in the signature of some groups $\hat{\Gamma}_{0,p}(p)$ and $\hat{\Gamma}_{0,p}(p^2), p$ is a prime number, and the number of link periods were found.
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Cite This Article
ÜNLÜYOL, E., BÜYÜKKARAGÖZ, A. (2020). The Signatures and Boundary Components of the Groups $\hat{\Gamma}_{0,n}(N)$. Turkish Journal of Science, Cilt: 5 - Sayı: 3, 268–279. https://ajindex.com/articles/809485