Extending generalized quadrangles (Q1118161)

Let P be any point of a finite incidence structure S and denote by \(S_ P\) the incidence structure which consists of all points of S joined to P and all lines of S containing P. S is called an extended generalized quadrangle of order (s,t) if S is connected and \(S_ P\) is a generalized quadrangle of order (s,t) for all points P of S. The author investigates extended generalized quadrangles which are either 2-designs or locally polar spaces and finds some bounds on the parameters of S. Example: If S is a 2-design then s is even and \(s+2\) divides \((2t-1)2t(t+1).\)