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Dihedral Groups of order $2p$ of Automorphisms of Compact Riemann Surfaces of Genus $p-1$

  • Qingjie Yang,
    Department of Mathematics, Renmin University of China , Beijing, China, 100872
  • Weiting Zhong,
    Department of Mathematics, Renmin University of China , Beijing, China, 100872
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Abstract

In this paper we prove that there is only one conjugacy class of dihedral group of order $2p$ in the $2(p-1)\times 2(p-1)$ integral symplectic group 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: dihedral group, automorphism group, Riemann surface, integral symplectic matrix, fundamental domain dihedral group, automorphism group, Riemann surface, integral symplectic matrix, fundamental domain
MSC Classifications: 20H25, 57M60 show english descriptions Other matrix groups over rings
Group actions in low dimensions
20H25 - Other matrix groups over rings
57M60 - Group actions in low dimensions
 

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