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

Ferreira, Jorge N.M. and 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:https://doi.org/10.1016/j.jsc.2016.02.013) (Access to this publication is currently restricted. You may be able to access a copy if URLs are provided)

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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
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: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics
Depositing User: Peter Fleischmann
Date Deposited: 22 Mar 2016 12:20 UTC
Last Modified: 21 Nov 2017 16:40 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/54595 (The current URI for this page, for reference purposes)
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