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    Abstract hyperovals, partial geometries, and transitive hyperovals

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    http://hdl.handle.net/10217/167107
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    Abstract
    A hyperoval is a (q+2)- arc of a projective plane π, of order q with q even. Let G denote the collineation group of π containing a hyperoval Ω. We say that Ω is transitive if for any pair of points x, y is an element of Ω, there exists a g is an element of G fixing Ω setwise such that xg = y. In1987, Billotti and Korchmaros proved that if 4||G|, then either Ω is the regular hyperoval in PG(2,q) for q=2 or 4 or q = 16 and |G||144. In 2005, Sonnino proved that if |G| = 144, then π is desarguesian and Ω is isomorphic to the Lunelli-Sce hyperoval. For our main result, we show that if G is the ...
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    Author(s)
    Cooper, Benjamin C.

    Advisor(s)
    Penttila, Timothy

    Date Issued
    2015
    Format
    born digital; doctoral dissertations
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    • 2000-2019 - CSU Theses and Dissertations
    • Theses and Dissertations - Department of Mathematics

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