On monomial flocks

We study monomial flocks of quadratic cones of PG(3, q), with emphasis on the case where the flock is semifield, providing some nonexistence and some uniqueness results. In addition, we give a computer-free proof of the existence of the sporadic semifield flock of the quadratic cone of PG(3, 3(5)) (and hence of the sporadic translation ovoid of Q(4, 3(5))), and relate that flock to the sporadic simple group M-11. (C) 2001 Academic Press.