For even q, a group G isomorphic to PSL(2, q) stabilizes a Baer conic inside a symplectic subquadrangle W(3, q) of H(3, q^2). In this paper the action of G on points and lines of H(3, q^2) is investigated. A construction is given of an infinite family of hyperovals of size 2(q^3−q) of H(3, q^2), with each hyperoval having the property that its automorphism group contains G. Finally it is shown that the hyperovals constructed are not isomorphic to known hyperovals.
Hyperovals of H(3,q^2) when q is even
MARINO, Giuseppe
2013
Abstract
For even q, a group G isomorphic to PSL(2, q) stabilizes a Baer conic inside a symplectic subquadrangle W(3, q) of H(3, q^2). In this paper the action of G on points and lines of H(3, q^2) is investigated. A construction is given of an infinite family of hyperovals of size 2(q^3−q) of H(3, q^2), with each hyperoval having the property that its automorphism group contains G. Finally it is shown that the hyperovals constructed are not isomorphic to known hyperovals.File in questo prodotto:
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