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Symmetries of Riemann Surfaces on Which PSL(2,q) Acts as a Hurwitz Automorphism Group
Faculty Publications - Mathematics
  • S. Allen Broughton, Rose-Hulman Institute of Technology
  • Emilio Bujalance, Universidad Nacional de Educación a Distancia
  • Antonio F. Costa, Universidad Nacional de Educación a Distancia
  • Jose Manuel Gamboa, Universidad Autonoma de Madrid
  • Grzegorz Gromadzki, University of Gdansk,
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Let X be a compact Riemann surface and Aut(X) be its automorphism group. An automorphism of order 2 reversing the orientation is called a symmetry. The authors together with D. Singerman have been working on symmetries of Riemann surfaces in the last decade. In this paper, the symmetry type St(X) of X is defined as an unordered list of species of conjugacy classes of symmetries of X, and for a class of particular surfaces, St(X) is found. This class consists of Riemann surfaces on which PSL(2,q) acts as a Hurwitz group. An algorithm to calculate the symmetry type of this class is provided.

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Broughton, S.A., Bujalance, E., Costa, A.F., Gamboa, J.M., & Gromadzki, G. (1996). Symmetries of Riemann surfaces on which PSL(2.q) acts as a Hurwitz automorphism group. In Journal of Pure and Applied Algebra, 106, 113-126.