Generalized quadrangles with an ovoid that is translation with respect to opposite flags.

Autor: Alan Offer, Koen Thas, Hendrik Van Maldeghem
Zdroj: Archiv der Mathematik; Apr2005, Vol. 84 Issue 4, p375-384, 10p
Abstrakt: Abstract. The article [6] contains the result that if a finite generalized quadrangle G of order s has an ovoid $\mathcal{O}$ that is translation with respect to two opposite flags, but not with respect to any two non-opposite flags, then G is self-polar and $\mathcal{O}$ is the set of absolute points of a polarity. In particular, if G is the classical generalized quadrangle Q(4, q) then $\mathcal{O}$ is a Suzuki-Tits ovoid. In this article, we remove the need to assume that G is Q(4, q) in order to conclude that $\mathcal{O}$ is a Suzuki-Tits ovoid by showing that the initial assumptions in fact imply that G is Q(4, q). At the same time, we also relax the requirement that G have order s. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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