The classification of normalizing groups
Autor(a) principal: | |
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Data de Publicação: | 2013 |
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/10400.2/3812 |
Resumo: | Let X be a finite set such that |X|=n. Let Tn and Sn denote the transformation monoid and the symmetric group on n points, respectively. Given a∈Tn∖Sn, we say that a group G⩽Sn is a-normalizing if <a,G〉∖G=〈g−1ag|g∈G>,where a, G and g−1ag | g ∈ G denote the subsemigroups of Tn generated by the sets {a} ∪ G and {g−1ag | g ∈ G}, respectively. If G is a-normalizing for all a ∈ Tn \ Sn, then we say that G is normalizing.The goal of this paper is to classify the normalizing groups and hence answer a question of Levi, McAlister, and McFadden. The paper ends with a number of problems for experts in groups, semigroups and matrix theory. |
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The classification of normalizing groupsTransformation semigroupsPermutation groupsPrimitive groupsGAPLet X be a finite set such that |X|=n. Let Tn and Sn denote the transformation monoid and the symmetric group on n points, respectively. Given a∈Tn∖Sn, we say that a group G⩽Sn is a-normalizing if <a,G〉∖G=〈g−1ag|g∈G>,where a, G and g−1ag | g ∈ G denote the subsemigroups of Tn generated by the sets {a} ∪ G and {g−1ag | g ∈ G}, respectively. If G is a-normalizing for all a ∈ Tn \ Sn, then we say that G is normalizing.The goal of this paper is to classify the normalizing groups and hence answer a question of Levi, McAlister, and McFadden. The paper ends with a number of problems for experts in groups, semigroups and matrix theory.Repositório AbertoAraújo, JoãoCameron, Peter J.Mitchell, James D.Max, Neunhöffer2015-03-24T15:49:07Z20132013-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/3812engAraújo, João [et al.] - The classification of normalizing groups. "Journal of Algebra" [Em linha]. ISSN 0021-8693. Vol. 373 (2013), p. 1-110021-869310.1016/j.jalgebra.2012.08.033info: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:RCAAP2023-11-16T15:19:10Zoai:repositorioaberto.uab.pt:10400.2/3812Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:44:59.799321Repositório 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 classification of normalizing groups |
title |
The classification of normalizing groups |
spellingShingle |
The classification of normalizing groups Araújo, João Transformation semigroups Permutation groups Primitive groups GAP |
title_short |
The classification of normalizing groups |
title_full |
The classification of normalizing groups |
title_fullStr |
The classification of normalizing groups |
title_full_unstemmed |
The classification of normalizing groups |
title_sort |
The classification of normalizing groups |
author |
Araújo, João |
author_facet |
Araújo, João Cameron, Peter J. Mitchell, James D. Max, Neunhöffer |
author_role |
author |
author2 |
Cameron, Peter J. Mitchell, James D. Max, Neunhöffer |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Repositório Aberto |
dc.contributor.author.fl_str_mv |
Araújo, João Cameron, Peter J. Mitchell, James D. Max, Neunhöffer |
dc.subject.por.fl_str_mv |
Transformation semigroups Permutation groups Primitive groups GAP |
topic |
Transformation semigroups Permutation groups Primitive groups GAP |
description |
Let X be a finite set such that |X|=n. Let Tn and Sn denote the transformation monoid and the symmetric group on n points, respectively. Given a∈Tn∖Sn, we say that a group G⩽Sn is a-normalizing if <a,G〉∖G=〈g−1ag|g∈G>,where a, G and g−1ag | g ∈ G denote the subsemigroups of Tn generated by the sets {a} ∪ G and {g−1ag | g ∈ G}, respectively. If G is a-normalizing for all a ∈ Tn \ Sn, then we say that G is normalizing.The goal of this paper is to classify the normalizing groups and hence answer a question of Levi, McAlister, and McFadden. The paper ends with a number of problems for experts in groups, semigroups and matrix theory. |
publishDate |
2013 |
dc.date.none.fl_str_mv |
2013 2013-01-01T00:00:00Z 2015-03-24T15:49:07Z |
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/10400.2/3812 |
url |
http://hdl.handle.net/10400.2/3812 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Araújo, João [et al.] - The classification of normalizing groups. "Journal of Algebra" [Em linha]. ISSN 0021-8693. Vol. 373 (2013), p. 1-11 0021-8693 10.1016/j.jalgebra.2012.08.033 |
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.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 |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
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 |
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1799135021432307712 |