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dc.contributor.author
Brude, Javier Eugenio  
dc.contributor.author
Sasyk, Roman  
dc.date.available
2023-07-04T13:33:29Z  
dc.date.issued
2022-07  
dc.identifier.citation
Brude, Javier Eugenio; Sasyk, Roman; Permanence properties of verbal products and verbal wreath products of groups; European Mathematical Society; Groups Geometry And Dynamics; 16; 2; 7-2022; 363-401  
dc.identifier.issn
1661-7207  
dc.identifier.uri
http://hdl.handle.net/11336/202222  
dc.description.abstract
By means of analyzing the notion of verbal products of groups, we show that soficity, hyperlinearity, amenability, the Haagerup property, the Kazhdan property (T), and exactness are preserved under taking k-nilpotent products of groups, while being orderable is not preserved. We also study these properties for solvable and for Burnside products of groups. We then show that if two discrete groups are sofic, or have the Haagerup property, their restricted verbal wreath product arising from nilpotent, solvable, and certain Burnside products is also sofic or has the Haagerup property, respectively. We also prove related results for hyperlinear, linear sofic, and weakly sofic approximations. Finally, we give applications combining our work with the Shmelkin embedding to show that certain quotients of free groups are sofic or have the Haagerup property.  
dc.format
application/pdf  
dc.language.iso
eng  
dc.publisher
European Mathematical Society  
dc.rights
info:eu-repo/semantics/openAccess  
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/  
dc.subject
VERBAL PRODUCTS OF GROUPS  
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VERBAL WREATH PRODUCTS  
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SOFIC GROUPS  
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HYPERLINEAR GROUPS  
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LINEAR SOFIC GROUPS  
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WEAKLY SOFIC GROUPS  
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HAAGERUP PROPERTY  
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KAZHDAN’S PROPERTY (T)  
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EXACT GROUPS  
dc.subject.classification
Matemática Pura  
dc.subject.classification
Matemáticas  
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS  
dc.title
Permanence properties of verbal products and verbal wreath products of groups  
dc.type
info:eu-repo/semantics/article  
dc.type
info:ar-repo/semantics/artículo  
dc.type
info:eu-repo/semantics/publishedVersion  
dc.date.updated
2023-06-16T18:00:04Z  
dc.journal.volume
16  
dc.journal.number
2  
dc.journal.pagination
363-401  
dc.journal.pais
Suiza  
dc.description.fil
Fil: Brude, Javier Eugenio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina  
dc.description.fil
Fil: Sasyk, Roman. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina  
dc.journal.title
Groups Geometry And Dynamics  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://ems.press/journals/ggd/articles/6446556  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.4171/GGD/665  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1909.07800