Suzuki groups, one-factorizations and Lüneberg planes (Q1356403)

All one-factorizations of the complete graph on \(q^2\), \(q=2^{2e+1}\), vertices admitting the one point stabilizer of the Suzuki group Sz\((q)\) as an automorphism group and having \(q-1\) prescribed one-factors are determined. These arise from the involutions in the group. Moreover, a method is described for studying translation planes of (even) order \(q^2\) admitting Sz\((q)\) as a collineation group fixing an oval and acting 2-transitively on its points. This method is based on the possibility to describe a projective plane with an oval by means of one-factorizations of certain complete graphs. Since the results obtained for the one-factorizations are suitable for computer calculations, the authors are able to give a characterization of the Lüneburg plane of order 64 (\(q=8\)).