The invariant fields of the Sylow groups of classical groups in the natural characteristic

Ferreira, Jorge N. M.; Fleischmann, Peter

http://hdl.handle.net/10400.13/5032

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Authors

Ferreira, Jorge N. M.

Fleischmann, Peter

Abstract(s)

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.

Keywords

Finite classical groups Invariant fields Modular invariant theory Sylow groups . Faculdade de Ciências Exatas e da Engenharia

URI

http://hdl.handle.net/10400.13/5032

Citation

Jorge N. M. Ferreira & Peter Fleischmann (2016) The Invariant Fields of the Sylow Groups of Classical Groups in the Natural Characteristic, Communications in Algebra, 44:3, 977-1010, DOI: 10.1080/00927872.2014.999922