Metric approximations of unrestricted wreath products when the acting group is amenable

Autores
Brude, Javier Eugenio; Sasyk, Roman
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We give a simple and unified proof showing that the unrestricted wreath product of a weakly sofic, sofic, linear sofic, or hyperlinear group by an amenable group is weakly sofic, sofic, linear sofic, or hyperlinear, respectively. By means of the Kaloujnine-Krasner theorem, this implies that group extensions with amenable quotients preserve the four aforementioned metric approximation properties. We also discuss the case of co-amenable groups.
Fil: Brude, Javier Eugenio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Sasyk, Roman. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Materia
AMENABLE GROUPS
HYPERLINEAR GROUPS
LINEAR SOFIC GROUPS
SOFIC GROUPS
UNRESTRICTED WREATH PRODUCTS
WEAKLY SOFIC GROUPS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/149999
Acceder
id CONICETDig_1a8e671abab30e206c4c689f84a31570
oai_identifier_str oai:ri.conicet.gov.ar:11336/149999
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Metric approximations of unrestricted wreath products when the acting group is amenableBrude, Javier EugenioSasyk, RomanAMENABLE GROUPSHYPERLINEAR GROUPSLINEAR SOFIC GROUPSSOFIC GROUPSUNRESTRICTED WREATH PRODUCTSWEAKLY SOFIC GROUPShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We give a simple and unified proof showing that the unrestricted wreath product of a weakly sofic, sofic, linear sofic, or hyperlinear group by an amenable group is weakly sofic, sofic, linear sofic, or hyperlinear, respectively. By means of the Kaloujnine-Krasner theorem, this implies that group extensions with amenable quotients preserve the four aforementioned metric approximation properties. We also discuss the case of co-amenable groups.Fil: Brude, Javier Eugenio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Sasyk, Roman. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaTaylor & Francis2021-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/149999Brude, Javier Eugenio; Sasyk, Roman; Metric approximations of unrestricted wreath products when the acting group is amenable; Taylor & Francis; Communications In Algebra; 2021; 9-2021; 1-130092-7872CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.tandfonline.com/doi/full/10.1080/00927872.2021.1976790info:eu-repo/semantics/altIdentifier/doi/10.1080/00927872.2021.1976790info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2004.05735info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:59:32Zoai:ri.conicet.gov.ar:11336/149999instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:59:33.056CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Metric approximations of unrestricted wreath products when the acting group is amenable
title Metric approximations of unrestricted wreath products when the acting group is amenable
spellingShingle Metric approximations of unrestricted wreath products when the acting group is amenable
Brude, Javier Eugenio
AMENABLE GROUPS
HYPERLINEAR GROUPS
LINEAR SOFIC GROUPS
SOFIC GROUPS
UNRESTRICTED WREATH PRODUCTS
WEAKLY SOFIC GROUPS
title_short Metric approximations of unrestricted wreath products when the acting group is amenable
title_full Metric approximations of unrestricted wreath products when the acting group is amenable
title_fullStr Metric approximations of unrestricted wreath products when the acting group is amenable
title_full_unstemmed Metric approximations of unrestricted wreath products when the acting group is amenable
title_sort Metric approximations of unrestricted wreath products when the acting group is amenable
dc.creator.none.fl_str_mv Brude, Javier Eugenio
Sasyk, Roman
author Brude, Javier Eugenio
author_facet Brude, Javier Eugenio
Sasyk, Roman
author_role author
author2 Sasyk, Roman
author2_role author
dc.subject.none.fl_str_mv AMENABLE GROUPS
HYPERLINEAR GROUPS
LINEAR SOFIC GROUPS
SOFIC GROUPS
UNRESTRICTED WREATH PRODUCTS
WEAKLY SOFIC GROUPS
topic AMENABLE GROUPS
HYPERLINEAR GROUPS
LINEAR SOFIC GROUPS
SOFIC GROUPS
UNRESTRICTED WREATH PRODUCTS
WEAKLY SOFIC GROUPS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We give a simple and unified proof showing that the unrestricted wreath product of a weakly sofic, sofic, linear sofic, or hyperlinear group by an amenable group is weakly sofic, sofic, linear sofic, or hyperlinear, respectively. By means of the Kaloujnine-Krasner theorem, this implies that group extensions with amenable quotients preserve the four aforementioned metric approximation properties. We also discuss the case of co-amenable groups.
Fil: Brude, Javier Eugenio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Sasyk, Roman. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
description We give a simple and unified proof showing that the unrestricted wreath product of a weakly sofic, sofic, linear sofic, or hyperlinear group by an amenable group is weakly sofic, sofic, linear sofic, or hyperlinear, respectively. By means of the Kaloujnine-Krasner theorem, this implies that group extensions with amenable quotients preserve the four aforementioned metric approximation properties. We also discuss the case of co-amenable groups.
publishDate 2021
dc.date.none.fl_str_mv 2021-09
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/149999
Brude, Javier Eugenio; Sasyk, Roman; Metric approximations of unrestricted wreath products when the acting group is amenable; Taylor & Francis; Communications In Algebra; 2021; 9-2021; 1-13
0092-7872
CONICET Digital
CONICET
url http://hdl.handle.net/11336/149999
identifier_str_mv Brude, Javier Eugenio; Sasyk, Roman; Metric approximations of unrestricted wreath products when the acting group is amenable; Taylor & Francis; Communications In Algebra; 2021; 9-2021; 1-13
0092-7872
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.tandfonline.com/doi/full/10.1080/00927872.2021.1976790
info:eu-repo/semantics/altIdentifier/doi/10.1080/00927872.2021.1976790
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2004.05735
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Taylor & Francis
publisher.none.fl_str_mv Taylor & Francis
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1842269586527879168
score 13.13397

Publicaciones similares