The conjugacy problem in automaton groups is not solvable

(Free abelian)-by-free, self-similar groups generated by finite self-similar sets of tree automorphisms and having unsolvable conjugacy problem are constructed. Along the way, finitely generated, orbit undecidable, free subgroups of GLd(Z), for d⩾6, and Aut(Fd), for d⩾5, are constructed as well.

Detalles Bibliográficos
Autores: Šunic, Z., Ventura Capell, Enric|||0000-0003-3519-4135
Tipo de recurso: artículo
Fecha de publicación:2012
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/16507
Acceso en línea:https://hdl.handle.net/2117/16507
https://dx.doi.org/10.1016/j.jalgebra.2012.04.014
Access Level:acceso abierto
Palabra clave:Associative algebras
Group theory
Free abelian-by-free groups
Automaton groups
Conjugacy problem
Orbit decidability
Àlgebres associatives
Grups, Teoria de
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
Descripción
Sumario:(Free abelian)-by-free, self-similar groups generated by finite self-similar sets of tree automorphisms and having unsolvable conjugacy problem are constructed. Along the way, finitely generated, orbit undecidable, free subgroups of GLd(Z), for d⩾6, and Aut(Fd), for d⩾5, are constructed as well.