Real genus actions of finite simple groups

A finite group G can be represented as a group of dianalytic automorphisms of a, compact bordered Klein surface, that is, G acts effectively on a bord ered surface. The real genus rho (G) is the minimum algebraic genus of any bordered surface on which G acts. A real genus action of G is an action of G on a bordered surface of (algebraic) genus rho (G). In this paper we cons ider real genus actions of finite simple groups. Let G be a finite simple g roup, and let X be a bordered surface of least genus on which G acts. We sh ow that if G is (2, s, t)-generated, then G is normal in Ant (X), [Ant X : G] divides 4, and Ant X embeds faithfully in Ant G. We also consider the re al genus actions of each projective special linear group PSL (2, q).