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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.

##### MSC:
 30F10 Compact Riemann surfaces and uniformization 20F29 Representations of groups as automorphism groups of algebraic systems
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