Generating symplectic and hermitian dual polar spaces over arbitrary fields nonisomorphic to F2

Cooperstein [6], [7] proved that every finite symplectic dual polar space DW (2n-1,q), q not equal 2, can be generated by ((2nn)(n))-((2n)(n-)) points and that every finite Hermitian dual polar space DH(2n-1,q(2)), q not equal 2, can be generated by ((2n)(n)) points. In the present paper, we show that these conclusions remain valid for symplectic and Hermitian dual polar spaces over in finite fields. A consequence of this is that every Grassmann-embedding of asymplectic or Hermitian dual polar space is absolutely universal if the (possibly infinite) underlying field has size at least 3.