The Symmetric Genus of the Mathieu Groups

The (symmetric) genus of a finite group may be defined as thesmallest genus of those closed orientable surfaces on whichG acts faithfully as a group of automorphisms. In this paperthe genus of each of the five Mathieu groups M₁₁, M₁₂, M₂₂,M₂₃ and M₂₄ is determined, with the help of some computer calculationsand a little-known of Ree on permutations.