The invariant rings of the Sylow groups of \(GU (3,q^{2})\), \(GU(4,q^{2})\), \(Sp(4,q)\) and \(O^{+}(4,q)\) in the natural characteristic
In the paper under review, the authors construct a presentation for the invariant ring of \(G\) acting on natural module, where \(G\) stands for a Sylow \(p\)-subgroup of the unitary groups \(GU(3,q^2)\), \(GU(4,q^2)\), the symplectic group \(Sp(4,q)\) and, for \(q\) odd, the orthogonal group \(O^+(4,q)\). They prove that these rings are generated by orbit products of variables and certain invariant polynomials, and these generators form a \(SAGBI\) basis and the invariant ring for \(G\) is a complete intersection.
scientific article; zbMATH DE number 6680376