GGS-groups over primary trees: branch structures

We study branch structures in Grigorchuk–Gupta–Sidki groups (GGS-groups) over primary trees, that is, regular rooted trees of degree pn for a prime p. Apart from a small set of exceptions for p=2, we prove that all these groups are weakly regular branch over G′′. Furthermore, in most cases they are...

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Detalles Bibliográficos
Autores: Di Domenico, Elena, Fernández Alcober, Gustavo Adolfo, Gavioli, N.
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universidad del País Vasco
Repositorio:Addi. Archivo Digital para la Docencia y la Investigación
OAI Identifier:oai:addi.ehu.eus:10810/61079
Acceso en línea:http://hdl.handle.net/10810/61079
Access Level:acceso abierto
Palabra clave:group theory
automorphisms of rooted trees
branch groups
weakly branch groups
Descripción
Sumario:We study branch structures in Grigorchuk–Gupta–Sidki groups (GGS-groups) over primary trees, that is, regular rooted trees of degree pn for a prime p. Apart from a small set of exceptions for p=2, we prove that all these groups are weakly regular branch over G′′. Furthermore, in most cases they are actually regular branch over γ3(G). This is a significant extension of previously known results regarding periodic GGS-groups over primary trees and general GGS-groups in the case n=1. We also show that, as in the case n=1, a GGS-group generated by a constant vector is not branch.