Sublines of Prime Order Contained in the Set of Internal Points of a Conic |
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Authors: | Michel Lavrauw |
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Institution: | (1) Departament of Discrete Mathematics, Technische Universiteit Eindhoven, HG 9.55, PO Box 513, 5600, MB, The Netherlands |
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Abstract: | In 2] it was shown that if q ≥ 4n2−8n+2 then there are no subplanes of order q contained in the set of internal points of a conic in PG(2,qn), q odd, n≥ 3. In this article we improve this bound in the case where q is prime to
, and prove a stronger theorem by considering sublines instead of subplanes. We also explain how one can apply this result
to flocks of a quadratic cone in PG(3,qn), ovoids of Q(4,qn), rank two commutative semifields, and eggs in PG(4n−1,q).
AMS Classification:11T06, 05B25, 05E12, 51E15 |
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Keywords: | internal points of a conic flock ovoid egg semifield |
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