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A Distance-2-Spread of the Generalized Hexagon H(3)
A. De Wispelaere and H. Van Maldeghem
Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281-S22, 9000 Gent, Belgium
{adw, hvm}@cage.rug.ac.be
Annals of Combinatorics 8 (2) p.133-154 June, 2004
AMS Subject Classification: 51E12
In this paper, we construct a distance-2-spread of the known generalized hexagon of order 3 (the split Cayley hexagon H(3)). Furthermore we prove the uniqueness of this distance-2-spread in H(3) and show that its automorphism group is the linear group L2(13). We remark that a distance-2-spread in any split Cayley hexagon H(q) is a line spread of the underlying polar space Q(6, q) and we construct a line spread of Q(6, 2) that is not a distance-2-spread in any H(2) defined on Q(6, 2).
Keywords: generalized hexagon, ovoid, spread, colouring, matching


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