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Dihedral Groups of Order 2p of Automorphisms of Compact Riemann Surfaces of Genus p – 1

Published online by Cambridge University Press:  20 November 2018

Qingjie Yang  and
Weiting Zhong
Qingjie Yang
Affiliation:
Department of Mathematics, Renmin University of China, Beijing, China, 100872. e-mail: yangqj@ruc.edu.cn, e-mail: zhwt 2007@yahoo.com.cn
Weiting Zhong
Affiliation:
Department of Mathematics, Renmin University of China, Beijing, China, 100872. e-mail: yangqj@ruc.edu.cn, e-mail: zhwt 2007@yahoo.com.cn
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Abstract

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In this paper we prove that there is only one conjugacy class of dihedral group of order $2p$ in the $2\left( p\,-\,1 \right)\,\times \,2\left( p\,-\,1 \right)$ integral symplectic group that can be realized by an analytic automorphism group of compact connected Riemann surfaces of genus $p\,-\,1$. A pair of representative generators of the realizable class is also given.

Keywords

20H2557M60dihedral groupautomorphism groupRiemann surfaceintegral symplectic matrixfundamental domain
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 58 , Issue 1 , 01 March 2015 , pp. 196 - 206
Copyright
Copyright © Canadian Mathematical Society 2015

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