Abstract
In this paper we give a method for studying a plane of order q 2 admitting Sz( q) as a collineation group fixing an oval and acting 2-transitively on its points; we prove in particular that for q = 8 the dual Lüneburg plane is the unique plane with this property. We also determine all one-factorizations of the complete graph on q 2 vertices admitting the one-point-stabilizer of Sz( q) as an automorphism group and having q − 1 prescribed one-factors.
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