The Invariant Fields of the Sylow Groups of Classical Groups in the Natural Characteristic. Issue 3 (3rd March 2016)

• Record Type: Journal Article
• Authors: Ferreira, Jorge N. M.; Fleischmann, Peter
• Is Part Of: Communications in algebra. Volume 44:Issue 3(2016)
• Page Start: 977
• Page End: 1010
• Publication Date: 2016-03-03
• Subjects: Finite classical groups -- Invariant fields -- Modular invariant theory -- Sylow groups; Primary: 13A50; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2014.999922
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract : Let X be any finite classical group defined over a finite field of characteristic p > 0. In this article, we determine the fields of rational invariants for the Sylow p -subgroups of X, acting on the natural module. In particular, we prove that these fields are generated by orbit products of variables and certain invariant polynomials which are images under Steenrod operations, applied to the respective invariant linear forms defining X .