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
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.13/5033 |
Resumo: | 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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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/10400.13/5033engFerreira, J. N., & Fleischmann, P. (2017). 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, 356-371.10.1016/j.jsc.2016.02.013info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-02-19T04:42:56Zoai:digituma.uma.pt:10400.13/5033Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T16:46:58.699897Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
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 |
Ferreira, J. N., & Fleischmann, P. (2017). 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, 356-371. 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:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799130941730324480 |