Let H be a geometric hyperplane of a classical finite generalized quadrangle Q and let C = Q H be its complement in Q, viewed as a point-line geometry. We shall prove that C admits a flag-transitive automorphism group if and only if H spans a hyperplane of the projective space in which Q is naturally embedded (but with Q viewed as Q(4, q) when Q = W(q), q even). Furthermore, if Q is the dual of Ii(4, q(2)) and H, C are as above, then C is flag-transitive if and only if H = p(perpendicular to) for some point p of Q.

Pasini, A., & Shpectorov, S. (1999). Flag-transitive hyperplane complements of classical generalized quadrangles. BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY SIMON STEVIN, 6(4), 571-587 [10.36045/bbms/1103055583].

Flag-transitive hyperplane complements of classical generalized quadrangles

PASINI, ANTONIO;
1999

Abstract

Let H be a geometric hyperplane of a classical finite generalized quadrangle Q and let C = Q H be its complement in Q, viewed as a point-line geometry. We shall prove that C admits a flag-transitive automorphism group if and only if H spans a hyperplane of the projective space in which Q is naturally embedded (but with Q viewed as Q(4, q) when Q = W(q), q even). Furthermore, if Q is the dual of Ii(4, q(2)) and H, C are as above, then C is flag-transitive if and only if H = p(perpendicular to) for some point p of Q.
Pasini, A., & Shpectorov, S. (1999). Flag-transitive hyperplane complements of classical generalized quadrangles. BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY SIMON STEVIN, 6(4), 571-587 [10.36045/bbms/1103055583].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11365/17487
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