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Let X be any finite classical group defined over a finite field ofcharacteristic p>0. In this paper we determine the fields of rationalinvariants for the Sylow p-subgroups of X, acting on the natural module. Inparticular we prove that these fields are generated by orbit products ofvariables and certain invariant polynomials which are images under Steenrodoperations, applied to the respective invariant linear forms defining X.

The Invariant Fields of the Sylow groups of Classical Groups in the natural characteristic