Sublines of prime order contained in the set of internal points of a conic
In [2] it was shown that if q >= 4n(2) - 8n+2 then there are no subplanes of order q contained in the set of internal points of a conic in PG(2,q(n)), q odd, n >= 3. In this article we improve this bound in the case where q is prime to q > 2n(2)-(4-2 root 3)n + (3-2 root 3), 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,q(n)), ovoids of Q(4,q(n)), rank two commutative semifields, and eggs in PG(4n-1,q).
internal points of a conic flock ovoid semifield egg