Characterisations of flock quadrangles

C.M. O'Keefe, Tim Penttila

    Research output: Contribution to journalArticle

    6 Citations (Scopus)

    Abstract

    We characterise the Hermitian and Kantor flock generalized quadrangles of order (q(2), q), q even, (associated with the linear and Fisher-Thas-Walker flocks of a quadratic cone, and the Desarguesian and Betten-Walker translation planes) in terms of a self-dual subquadrangle. Equivalently, we show that a herd which contains a translation oval must be associated with the linear or Fisher-Thas-Walker flock. This result is a consequence of the determination of all functions which satisfy a certain absolute trace equation whose form is remarkably similar to that of an equation arising in recent studies of ovoids in three-dimensional projective space of finite order q.
    Original languageEnglish
    Pages (from-to)171-191
    JournalGeometriae Dedicata
    Volume82
    Issue number1-3
    DOIs
    Publication statusPublished - 2000

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