Nilpotent symmetric Jacobian matrices and the Jacobian Conjecture II

It is shown that the Jacobian Conjecture holds for all polynomial maps F:kn→kn of the form F=x+H, such that JH is nilpotent and symmetric, when nless-than-or-equals, slant4. If H is also homogeneous a similar result is proved for all nless-than-or-equals, slant5.