The Invariant Fields of the Sylow groups of Classical Groups in the   natural characteristic
  Let X be any finite classical group defined over a finite field of characteristic p>0. In this paper we determine the fields of rational invariants for the Sylow p-subgroups of X, acting on the natural module. In particular we prove that these fields are generated by orbit products of variables and certain invariant polynomials which are images under Steenrod operations, applied to the respective invariant linear forms defining X. 
Jorge N.M. Ferreira, Peter Fleischmann
math.AC