Ferreira, Jorge N.M., Fleischmann, Peter (2016) 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. Journal of Symbolic Computation, 79 (Part 2). pp. 356-371. ISSN 0747-7171. E-ISSN 1095-855X. (doi:10.1016/j.jsc.2016.02.013) (KAR id:54595)
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Official URL: http://dx.doi.org/10.1016/j.jsc.2016.02.013 |
Abstract
Let G be a Sylow p -subgroup of the unitary groups GU(3,q2)GU(3,q2), GU(4,q2)GU(4,q2), the symplectic group Sp(4,q)Sp(4,q) and, for q odd, the orthogonal group O+(4,q)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.
Item Type: | Article |
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DOI/Identification number: | 10.1016/j.jsc.2016.02.013 |
Uncontrolled keywords: | Invariant rings; SAGBI bases; Modular invariant theory; Sylow subgroups; Finite classical groups |
Subjects: | Q Science > QA Mathematics (inc Computing science) > QA150 Algebra |
Divisions: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |
Depositing User: | Peter Fleischmann |
Date Deposited: | 22 Mar 2016 12:20 UTC |
Last Modified: | 17 Aug 2022 12:20 UTC |
Resource URI: | https://kar.kent.ac.uk/id/eprint/54595 (The current URI for this page, for reference purposes) |
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