The occurrence of finite simple permutation groups of fixity 2 as automorphism groups of Riemann surfaces

Abstract

Motivated by the theory of Riemann surfaces and specifically the significance of Weierstrass points, we study finite simple groups from a permutation action point of view. We classify all possibilities for finite simple groups acting faithfully on a compact Riemann surface of genus at least 2 in such a way that all non-trivial elements have at most two fixed points on each non-regular orbit and at most four fixed points in total.