Hyperbolic ovals in finite planes

The characterization of Rosati oval in any regular nearfield plane of dimension 2 over its center was presented. Rosati showed that every sharply 3-transitive permutation group gives rise to an affine plane containing hyperbolic ovals. For finite groups the degree of permutation group was found to be a prime power. It was observed that Rosati oval in the nearfield plane and its dual oval in the dual nearfield plane were the only hyperbolic ovals of dihydral type in non-Desarguesian plane of order 9