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

Bibliographic Details
Main Author: Ferreira, Jorge N. M.
Publication Date: 2017
Other Authors: Fleischmann, Peter
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10400.13/5033
Summary: Let G be a Sylow p-subgroup of the unitary groups GU(3, q2), GU(4, q2), the symplectic group Sp(4, q) and, for q odd, the orthogonal group O +(4, q). In this paper we construct a presenta tion 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.
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spelling The invariant rings of the Sylow groups of GU(3,q2), GU(4,q2), Sp(4,q) and O+(4,q) in the natural characteristicInvariant ringsSAGBI basesModular invariant theorySylow subgroupsFinite classical groups.Faculdade de Ciências Exatas e da EngenhariaLet G be a Sylow p-subgroup of the unitary groups GU(3, q2), GU(4, q2), the symplectic group Sp(4, q) and, for q odd, the orthogonal group O +(4, q). In this paper we construct a presenta tion 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.ElsevierDigitUMaFerreira, Jorge N. M.Fleischmann, Peter2023-02-13T16:09:40Z20172017-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.13/5033eng10.1016/j.jsc.2016.02.013info:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2025-02-24T16:55:30Zoai:digituma.uma.pt:10400.13/5033Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T20:43:01.401435Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv 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
title 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
spellingShingle 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.
Invariant rings
SAGBI bases
Modular invariant theory
Sylow subgroups
Finite classical groups
.
Faculdade de Ciências Exatas e da Engenharia
title_short 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
title_full 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
title_fullStr 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
title_full_unstemmed 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
title_sort 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
author Ferreira, Jorge N. M.
author_facet Ferreira, Jorge N. M.
Fleischmann, Peter
author_role author
author2 Fleischmann, Peter
author2_role author
dc.contributor.none.fl_str_mv DigitUMa
dc.contributor.author.fl_str_mv Ferreira, Jorge N. M.
Fleischmann, Peter
dc.subject.por.fl_str_mv Invariant rings
SAGBI bases
Modular invariant theory
Sylow subgroups
Finite classical groups
.
Faculdade de Ciências Exatas e da Engenharia
topic Invariant rings
SAGBI bases
Modular invariant theory
Sylow subgroups
Finite classical groups
.
Faculdade de Ciências Exatas e da Engenharia
description Let G be a Sylow p-subgroup of the unitary groups GU(3, q2), GU(4, q2), the symplectic group Sp(4, q) and, for q odd, the orthogonal group O +(4, q). In this paper we construct a presenta tion 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.
publishDate 2017
dc.date.none.fl_str_mv 2017
2017-01-01T00:00:00Z
2023-02-13T16:09:40Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.13/5033
url http://hdl.handle.net/10400.13/5033
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1016/j.jsc.2016.02.013
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
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institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
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