Generalised quadrangles with a group of automorphisms acting primitively   on points and lines
  We show that if G is a group of automorphisms of a thick finite generalised quadrangle Q acting primitively on both the points and lines of Q, then G is almost simple. Moreover, if G is also flag-transitive then G is of Lie type. 
John Bamberg, Michael Giudici, Joy Morris, Gordon F. Royle and Pablo   Spiga
math.CO