The Invariant Fields of the Sylow Groups of Classical Groups in the Natural Characteristic |
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| Authors: | Jorge N M Ferreira Peter Fleischmann |
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| Institution: | 1. Faculdade de Ciências Exatas e da Engenharia, Universidade da Madeira, Funchal, Portugalnelio@uma.pt;3. School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, United Kingdom |
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| 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. |
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| Keywords: | Finite classical groups Invariant fields Modular invariant theory Sylow groups |
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