Generalized Q-sets in a finite locally projective planar space

Generalized Q-sets in a locally projective planar space S of order n are defined. If S contains a non-degenerate generalized Q-set Q and the order n (>4) of S is even, we prove that S is embeddable in PG(3,n) and Q is isomorphic to an ovoid or a hyperbolic quadric of PG(3,n).