Simple groups acting on translation planes

Abstract

We discuss the possibility of finite simple groups acting as collineation groups on finite translation planes of odd order with special attention paid to the sporadic simple groups. We assume such a group acts irreducibly (in the vector space sense) on the plane. It is shown that if the characteristic of the plane does not divide the order of the group, then the group cannot be one of eleven sporadic simple groups. Also, if one of the Mathieu groups acts irreducibly on a finite translation plane then it is either M11 or M23.