Finite doubly transitive affine planes (Q1268615)

The authors classify all finite affine planes with a doubly transitive automorphism group (on the points). First they remark that such a plane is always a translation plane and that the ``solvable case'' has been treated by \textit{D. A. Foulser} already [Math. Z. 86, 191-204 (1964; Zbl 0144.01803)]. Then they apply a result of Hering, who classified non-solvable linear groups acting transitively on the non-zero vectors of a finite vector space. A case-by-case study finishes the classification. Besides the Desarguesian affine planes, one finds the Hall plane of order 9 and the Hering plane of order 27.