OVALS IN COMMUTATIVE SEMIFIELD PLANES

A translation plane pi coordinatized by a commutative semifield of odd order has an orthogonal polarity whose absolute points form a (parabo lic) oval SZ. Such parabolic ovals are 2-transitive, i.e. the collinea tion group of pi fixing Omega acts 2-transitively on the affine points of Omega. The main purpose of the present paper is to show that the c ommutative semifield planes are the only translation plane of odd orde r containing 2-transitive parabolic ovals.