On two-transitive parabolic ovals (Q557070)

Let \(G\) be a collineation group of a finite projective plane of odd order such that \(G\) preserves an oval \(\Omega\) in the plane, fixes a point \(P\in \Omega\) and acts doubly transitively on \(\Omega \setminus \{P\}\). The authors show that each involution in the center of a Sylow 2-subgroup of \(G\) is a homology.