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
文摘
Let G be a Sylow p -subgroup of the unitary groups dfd5516288f027b70f00888950a5ee08" title="Click to view the MathML source">GU(3,q2), GU(4,q2), the symplectic group dfd54ef53" title="Click to view the MathML source">Sp(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.