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Symmetries of Riemann surfaces on which \(\text{PSL}(2,q)\) acts as a Hurwitz automorphism group. (English) Zbl 0847.30026
Let \(X\) be a compact Riemann surface and \(\operatorname{Aut}(X)\) 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 \(\text{St}(X)\) of \(X\) is defined as an unordered list of species of conjugacy classes of symmetries of \(X\), and for a class of particular surfaces, \(\text{St}(X)\) is found. This class consists of Riemann surfaces on which \(\text{PSL}(2, q)\) acts as a Hurwitz group. An algorithm to calculate the symmetry type of this class is provided.

30F10 Compact Riemann surfaces and uniformization
20F29 Representations of groups as automorphism groups of algebraic systems
Full Text: DOI
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