ABSTRACT
Definition 74.1. Let O be an oval in a projective plane Π. Let ` be a tangent line and form the associated affine plane Π` by removing `. The O is said to be a ‘parabolic oval’ of Π`. The point of O on the line at infinity is called the ‘parabolic point’. We say that O is a ‘doubly transitive parabolic oval’ if and only if there is a collineation group of the affine plane that leaves O invariant and induces a doubly transitive group on the affine points of O.
