The conjugacy stability problem for parabolic subgroups in artin groups

Given an Artin group A and a parabolic subgroup P, we study if every two elements of P that are conjugate in A, are also conjugate in P. We provide an algorithm to solve this decision problem if A satisfies three properties that are conjectured to be true for every Artin group. This allows to solve...

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Detalles Bibliográficos
Autor: Cumplido Cabello, María
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2022
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/144840
Acceso en línea:https://hdl.handle.net/11441/144840
https://doi.org/10.1007/s00009-022-02153-9
Access Level:acceso abierto
Palabra clave:Artin groups
conjugacy stability
conjugacy classes
algorithmic in group theory
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spelling The conjugacy stability problem for parabolic subgroups in artin groupsCumplido Cabello, MaríaArtin groupsconjugacy stabilityconjugacy classesalgorithmic in group theoryGiven an Artin group A and a parabolic subgroup P, we study if every two elements of P that are conjugate in A, are also conjugate in P. We provide an algorithm to solve this decision problem if A satisfies three properties that are conjectured to be true for every Artin group. This allows to solve the problem for new families of Artin groups. We also partially solve the problem if A has FC-type, and we totally solve it if A is isomorphic to a free product of Artin groups of spherical type. In particular, we show that in this latter case, every element of A is contained in a unique minimal (by inclusion) parabolic subgroup.SpringerÁlgebra2022info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/144840https://doi.org/10.1007/s00009-022-02153-9reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésMEDITERRANEAN JOURNAL OF MATHEMATICS, 19 (5), 237-1.https://doi.org/10.1007/s00009-022-02153-9info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1448402026-06-17T12:51:07Z
dc.title.none.fl_str_mv The conjugacy stability problem for parabolic subgroups in artin groups
title The conjugacy stability problem for parabolic subgroups in artin groups
spellingShingle The conjugacy stability problem for parabolic subgroups in artin groups
Cumplido Cabello, María
Artin groups
conjugacy stability
conjugacy classes
algorithmic in group theory
title_short The conjugacy stability problem for parabolic subgroups in artin groups
title_full The conjugacy stability problem for parabolic subgroups in artin groups
title_fullStr The conjugacy stability problem for parabolic subgroups in artin groups
title_full_unstemmed The conjugacy stability problem for parabolic subgroups in artin groups
title_sort The conjugacy stability problem for parabolic subgroups in artin groups
dc.creator.none.fl_str_mv Cumplido Cabello, María
author Cumplido Cabello, María
author_facet Cumplido Cabello, María
author_role author
dc.contributor.none.fl_str_mv Álgebra
dc.subject.none.fl_str_mv Artin groups
conjugacy stability
conjugacy classes
algorithmic in group theory
topic Artin groups
conjugacy stability
conjugacy classes
algorithmic in group theory
description Given an Artin group A and a parabolic subgroup P, we study if every two elements of P that are conjugate in A, are also conjugate in P. We provide an algorithm to solve this decision problem if A satisfies three properties that are conjectured to be true for every Artin group. This allows to solve the problem for new families of Artin groups. We also partially solve the problem if A has FC-type, and we totally solve it if A is isomorphic to a free product of Artin groups of spherical type. In particular, we show that in this latter case, every element of A is contained in a unique minimal (by inclusion) parabolic subgroup.
publishDate 2022
dc.date.none.fl_str_mv 2022
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/144840
https://doi.org/10.1007/s00009-022-02153-9
url https://hdl.handle.net/11441/144840
https://doi.org/10.1007/s00009-022-02153-9
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv MEDITERRANEAN JOURNAL OF MATHEMATICS, 19 (5), 237-1.
https://doi.org/10.1007/s00009-022-02153-9
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.301603

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