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 Lueneburg 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.
Suzuki groups, one-factorizations and Lueneburg planes / Bonisoli, Arrigo; G., Korchmaros. - In: DISCRETE MATHEMATICS. - ISSN 0012-365X. - STAMPA. - 161:(1996), pp. 13-24.
Suzuki groups, one-factorizations and Lueneburg planes.
BONISOLI, Arrigo;
1996
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 Lueneburg 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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