The conjugacy problem in automaton groups is not solvable
Abstract
(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, orbit undecidable, free subgroups of GLd(Z), for d > 5, and Aut(Fd), for d > 4, are constructed as well.
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