Corpus ID: 67855910

# Orbits of Automaton Semigroups and Groups

@article{DAngeli2019OrbitsOA,
title={Orbits of Automaton Semigroups and Groups},
author={D. D'Angeli and Dominik Francoeur and E. Rodaro and Jan Philipp W{\"a}chter},
journal={ArXiv},
year={2019},
volume={abs/2007.10273}
}
We study the orbits of right infinite or $\omega$-words under the action of semigroups and groups generated by automata. We see that an automaton group or semigroup is infinite if and only if it admits an $\omega$-word with an infinite orbit, which solves an open problem communicated to us by Ievgen V. Bondarenko. In fact, we prove a generalization of this result, which can be applied to show that finitely generated subgroups and subsemigroups as well as principal left ideals of automaton… Expand
2 Citations

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