Extending partial flocks containing linear subflocks (Q1912000)

A flock on a quadratic cone in \(PG (3,q)\) is a partition of the points other than the vertex into disjoint irreducible conics. The flock is linear if the planes containing the conics share a common line. There has been much work on the relations between flocks, translation planes and generalized quadrangles. The main result of this paper is that if a partial flock properly contains a linear subflock with at least \((q - 1)/2\) conics then it may be extended uniquely to a linear or Fischer flock.