On the existence of free subsemigroups in reversible automata semigroups

Dominik Francoeur (1) , Ivan Mitrofanov

1 ENS de Lyon - École normale supérieure de Lyon

We prove that the semigroup generated by a reversible Mealy automaton contains a free subsemigroup of rank two if and only if it contains an element of infinite order.

Domaines: Théorie des groupes [math.GR]

Dominik Francoeur, Ivan Mitrofanov. On the existence of free subsemigroups in reversible automata semigroups. 2019. ⟨ensl-02409426⟩