Generalized Quadrangles and Transitive Pseudo-Hyperovals

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    © 2014 Wiley Periodicals, Inc. A pseudo-hyperoval of a projective space, q even, is a set of subspaces of dimension such that any three span the whole space. We prove that a pseudo-hyperoval with an irreducible transitive stabilizer is elementary. We then deduce from this result a classification of the thick generalized quadrangles that admit a point-primitive, line-transitive automorphism group with a point-regular abelian normal subgroup. Specifically, we show that is flag-transitive and isomorphic to, where is either the regular hyperoval of PG(2, 4) or the Lunelli-Sce hyperoval of PG(2, 16).
    Original languageEnglish
    Pages (from-to)151-164
    Number of pages14
    JournalJournal of Combinatorial Designs
    Issue number4
    Publication statusPublished - 1 Apr 2016


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