The invariant rings of the Sylow groups of \(GU (3,q^{2})\), \(GU(4,q^{2})\), \(Sp(4,q)\) and \(O^{+}(4,q)\) in the natural characteristic
type: Item
instance of: scholarly article
title: The invariant rings of the Sylow groups of \(GU (3,q^{2})\), \(GU(4,q^{2})\), \(Sp(4,q)\) and \(O^{+}(4,q)\) in the natural characteristic
zbMATH Open document ID: 1365.13008
author: Yong-Cai Geng
author: Sumit K. Garg
published in: Journal of Symbolic Computation
publication date: 2017-02-03T00:00:00Z
review text: In the paper under review, the authors construct a presentation for the invariant ring of \(G\) acting on natural module, where \(G\) stands for a Sylow \(p\)-subgroup of the unitary groups \(GU(3,q^2)\), \(GU(4,q^2)\), the symplectic group \(Sp(4,q)\) and, for \(q\) odd, the orthogonal group \(O^+(4,q)\). They prove that these rings are generated by orbit products of variables and certain invariant polynomials, and these generators form a \(SAGBI\) basis and the invariant ring for \(G\) is a complete intersection.
reviewed by: Şehmus Fındık
Mathematics Subject Classification ID: 13A50
Mathematics Subject Classification ID: 20G40
zbMATH DE Number: 6680376
zbMATH Keywords: invariant rings
zbMATH Keywords: \(SAGBI\) bases
zbMATH Keywords: modular invariant theory
zbMATH Keywords: Sylow subgroups
zbMATH Keywords: finite classical groups
describes a project that uses: Magma
MaRDI profile type: Publication
full work available at URL: j.jsc.2016.02.013
OpenAlex ID: W2304703944
cites work: Q4273960
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cites work: Modular invariant theory
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DOI: 10.1016/J.JSC.2016.02.013
description: scientific article; zbMATH DE number 6680376