AN EXTENSION OF WAGNER THEOREM

In his famous 1965 paper, Asher Wagner proves that if S is a finite affine plane and G a collineation group line transitive on S, then S is a translation affine plane and G contains the translation group of S. In this paper, we generalize Wagner's assumptions to: S is an affine space embedded as a maximal arc in a finite projective plane PI; G is a collineation group of PI-fixing S, fixing a line of PI-exterior to S, and line transitive on S. Under these assumptions we show that Wagner's conclusion still holds.