Finite simple groups acting with fixity 3 and their occurrence as groups of automorphisms of Riemann surfaces

The results in this article are based on the classification of finite simple groups that act with fixity 3. Motivated by the theory of Riemann surfaces, we investigate which ones of these groups act faithfully on a compact Riemann surface of genus at least 2 in such a way that all non-trivial elements have at most three fixed points on each non-regular orbit and at most four fixed points in total. In each case, we give detailed information about the possible branching data of the surface.