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THE HYPERPLANES OF $DW(5,q)$ WITH NO OVOIDAL QUAD

Published online by Cambridge University Press:  24 March 2006

BART DE BRUYN  and
HARM PRALLE
BART DE BRUYN
Affiliation:
Department of Pure Mathematics and Computer Algebra, Ghent University, Galglaan 2, B-9000 Gent, Belgium e-mail: [email protected]
HARM PRALLE
Affiliation:
Institute Computational Mathematics, Technische Universität Braunschweig, Pockelsstr. 14, 38106 Braunschweig, Germany e-mail: [email protected]
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Abstract

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Let $\Delta$ be one of the dual polar spaces $DW(5,q)$ or $DH(5,q^2)$. We consider a class of subspaces of $\Delta$, each member of which carries the structure of a near hexagon, and classify all these subspaces. Using this classification, we determine all hyperplanes of $DW(5,q)$ without ovoidal quads.

Keywords

51A5051E12
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 48 , Issue 1 , January 2006 , pp. 75 - 82
Copyright
2006 Glasgow Mathematical Journal Trust