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

  • Qingjie Yang (a1) and Weiting Zhong (a1)

In this paper we prove that there is only one conjugacy class of dihedral group of order 2p in the 2(p – 1) × 2(p – 1) 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.

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[1] Breuer, T., Characters and automorphism groups of compact Riemann surfaces. London Mathematical Society Lecture Note Series, 280, Cambridge University Press, Cambridge, 2000.
[2] Eckmann, B. and Müller, H., Plane motion groups and virtual Poincaré duality of dimension two. Invent. Math. 69 (1982), no. 2, 293310.
[3] Farkas, H. M. and Kra, I., Riemann surfaces. Second ed., Graduate Texts in Mathematics, 71, Springer-Verlag, New York, 1992.
[4] Gabai, D., Convergence groups are Fuchsian groups. Ann. of Math. 136 (1992), no. 3, 447510.
[5] George Michael, A. A., Metacyclic groups of automorphisms of compact Riemann surfaces. Hiroshima Math. J. 31 (2001), no. 1, 117132.
[6] Harvey, W. J., Spaces of discrete groups. In: Discrete groups and automorphic functions (Proc. Conf. Cambridge, 1975), Academic Press, London, 1977, pp. 295348..
[7] Jones, G. and Singerman, D., Complex functions. An algebraic and geometric viewpoint. Cambridge University Press, Cambridge, 1987.
[8] Kerckhoff, S. P., The Nielsen realization problem. Ann. of Math. 117 (1983), no. 2, 235265.
[9] Massey, W. S., Singular homology theory. Graduate Texts in Mathematics, 70, Spring-Verlag, New York-Berlin, 1980.
[10] Nielsen, J., Abbildungklassen Endliche Ordung. Acta Math. 75 (1943), 23115.
[11] Sjerve, D. and Yang, Q., Conjugacy classes of p-torsion in SPp-1(ℤ). J. Algebra 195 (1997), no. 2, 580603.
[12] Yang, Q., Dihedral groups of automorphisms of compact Riemann surfaces. Canad. Math. Bull. 41 (1998), no. 2, 252256.
[13] Yang, Q., Matrix classes realized by automorphisms of compact Riemann surfaces of genus two. Comm. Algebra 40 (2012), no. 7, 23432357.
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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