The conjugacy problem in automaton groups is not solvable
Zoran Sunic, Enric Ventura
TL;DR
This paper constructs specific automaton groups demonstrating that the conjugacy problem is unsolvable, and also establishes the existence of orbit undecidable free subgroups in certain linear and automorphism groups.
Contribution
It introduces new automaton groups with unsolvable conjugacy problems and constructs orbit undecidable free subgroups in GL_d(Z) and Aut(F_d).
Findings
Automaton groups with unsolvable conjugacy problem are constructed.
Orbit undecidable free subgroups in GL_d(Z) for d > 5 are constructed.
Orbit undecidable free subgroups in Aut(F_d) for d > 4 are constructed.
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 GL_d(Z), for d > 5, and Aut(F_d), for d > 4, are constructed as well.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Operator Algebra Research · Finite Group Theory Research