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)

• Record Type: Journal Article
• Authors: Ferreira, Jorge N.M.; Fleischmann, Peter
• Is Part Of: Journal of symbolic computation. Volume 79(2017)Part 2
• Page Start: 356
• Page End: 371
• Publication Date: 2017-03
• Subjects: Invariant rings -- SAGBI bases -- Modular invariant theory -- Sylow subgroups -- Finite classical groups; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2016.02.013
• Languages: English
• ISSNs: 0747-7171

Abstract

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.