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.

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Veröffentlicht in:	Journal of algebra 2012-08, Vol.364, p.148-154
Hauptverfasser:	Šunić, Zoran, Ventura, Enric
Format:	Artikel
Sprache:	eng
Schlagworte:	(Free abelian)-by-free groups Associative algebras Automaton groups Conjugacy problem Group theory Grups, Teoria de Matemàtiques i estadística Orbit decidability Teoria de grups Àlgebra Àlgebres associatives Àrees temàtiques de la UPC
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Beschreibung
Zusammenfassung:	(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.
ISSN:	0021-8693 1090-266X
DOI:	10.1016/j.jalgebra.2012.04.014