The uniqueness of Hering's translation plane of order 27 (Q1063865)

From the authors' abstract and introduction: ''It is shown that the following conjecture of \textit{M. J. Kallaher} and \textit{T. G. Ostrom} [Geom. Dedicata 9, 153-194 (1980; Zbl 0449.51003)] is correct: Hering's translation plane of order 27 is the only translation plane of odd dimension over its kernel which has a collineation group isomorphic to SL(2,w) with w prime to 5 and to the characteristic, and having no affine perspectivity. The main reduction of the conjecture has already been achieved by its authors, viz: Such a plane must have order 27 and w must be 13. In view of their results, the hypothesis on the dimension and on the non- existence of affine perspectivities is no longer needed to prove the conjecture. Our theorem is then the following: Theorem. Hering's translation plane of order 27 is the only translation plane of order 27 which admits SL(2,13) as a subgroup of its translation complement.''