The invariant rings of the Sylow groups of GU(3, q2), GU(4, q2), Sp(4, q) and O+(4, q) in the natural characteristic. (March 2017) - Ferreira, Jorge N.M.; Fleischmann, Peter
Abstract: Let G be a Sylow p -subgroup of the unitary groups G U ( 3, q 2 ), G U ( 4, q 2 ), the symplectic group S p ( 4, q ) and, for q odd, the orthogonal group O + ( 4, q ) . In this paper we construct a presentation for the invariant ring of G acting on the natural module. In particular we prove that these rings are generated by orbit products of variables and certain invariant polynomials which are images under Steenrod operations, applied to the respective invariant form defining the corresponding classical group. We also show that these generators form a SAGBI basis and the invariant ring for G is a complete intersection.