Generalized quadrangles in finite projective spaces

If a pointset of the projective spacePG(d,q), together with a lineset ofPG(d,q) form a generalized quadrangleS, thenS is of classical type. This beautiful theorem was proved by F. Buekenhout and C. Lefèvre. In this paper we give a simple proof of this theorem in the cased 4 (we suppose that the result is established ford = 3). We remark that in our proof a central role is played by the theory of subquadrangles.