Generalized \(Q\)-sets in a finite locally projective planar space (Q1808779)

The paper generalizes the notion of \(Q\)-set of a \(3\)-dimensional projective space and extends it to any finite locally projective planar space. If a locally projective planar space \(\mathcal S\) contains such a non-degenerate generalized \(Q\)-set \(Q\) and the order \(n \geq 4\) of \(\mathcal S\) is even, then it is proved that \(\mathcal{S}\) is embeddable in \(\text{PG}(3,n)\) and that \(Q\) is isomorphic to an ovoid or a hyperbolic quadric of \(\text{PG}(3,n)\).