Regular orbits for projective orthogonal groups over finite fields of odd characteristic (Q806040)

Let G be a permutation group acting on a finite set \(\Omega\). A subset \(\Delta\subset \Omega\) is called regular if only the identity of G fixes \(\Delta\) setwise. Obviously, a regular subset having k elements exists if and only if the set \(\Omega^ k\) has an orbit of length \(| G|\) (called regular orbit) under G. The author considers the projective orthogonal groups over a finite field GF(q), q odd, acting on the point set of the corresponding quadrics. She proves that these groups admit regular sets except for a finite number of cases in dimensions 2 and 3 and an explicit construction for representatives of regular orbits in the general case is described.