The Signatures and Boundary Components of the Groups $hat{Gamma}

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Turkish Journal of Science
Volume:5 Issue:3
The Signatures and Boundary Components of the Groups $hat{Gamma}_{0,n}(N)$

The Signatures and Boundary Components of the Groups $hat{Gamma}_{0,n}(N)$

Authors : Erdal ÜNLÜYOL, Aziz BÜYÜKKARAGÖZ

Pages : 268-279

View : 34 | Download : 10

Publication Date : 2020-12-30

Article Type : Research Paper

Abstract :In this paper, we established the group $\hat{\Gamma}_{0,n}insert ignore into journalissuearticles values(N);$ by group $\Gamma_{0,n}insert ignore into journalissuearticles values(N);$ 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 $\hat{\Gamma}_{0,p}insert ignore into journalissuearticles values(p);$ and $\hat{\Gamma}_{0,p}insert ignore into journalissuearticles values(p^2);, p$ is a prime number, and the number of link periods were found.
Keywords : Signature, Boundary component, Extended Modular Group, NEC Group, Hoare Uzzel Theorem

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