Residual properties of graph products of groups

We prove that the class of residually C groups is closed under taking graph products, provided that C is closed under taking subgroups, finite direct products and that free-by-C groups are residually C. As a consequence, we show that local embeddability into various classes of groups is stable under...

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Detalhes bibliográficos
Autores: Berlai, Federico, Ferov, Michal
Formato: artículo
Fecha de publicación:2016
País:España
Recursos:Universidad del País Vasco
Repositorio:Addi. Archivo Digital para la Docencia y la Investigación
OAI Identifier:oai:addi.ehu.eus:10810/72141
Acesso em linha:http://hdl.handle.net/10810/72141
Access Level:acceso abierto
Palavra-chave:graph products
residual properties
pro-C topology
local embeddability
residually amenable groups
Descrição
Resumo:We prove that the class of residually C groups is closed under taking graph products, provided that C is closed under taking subgroups, finite direct products and that free-by-C groups are residually C. As a consequence, we show that local embeddability into various classes of groups is stable under graph products. In particular, we prove that graph products of residually amenable groups are residually amenable, and that locally embeddable into amenable groups are closed under taking graph products.