Flag-transitive hyperplane complements in classical generalized quadrangles

A. Pasini*, S. Shpectorov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 H(4, q2) and H, C are as above, then C is flag-transitive if and only if H = p for some point p of Q.

Original languageEnglish
Pages (from-to)571-587
Number of pages17
JournalBulletin of the Belgian Mathematical Society - Simon Stevin
Volume6
Issue number4
DOIs
Publication statusPublished - 1999

Keywords

  • Generalized quadrangles
  • Maximal subgroup
  • Ovoids

ASJC Scopus subject areas

  • General Mathematics

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