The growth rates of automaton groups generated by reset automata

Abstract

We give sufficient conditions for when groups generated by automata in a class $\mathcal{C}$ of transducers, which contains the class of reset automata transducers, have infinite order. As a consequence we also demonstrate that if a group generated by an automata in $\mathcal{C}$ is infinite, then it contains a free semigroup of rank at least 2. This gives a new proof, in the context of groups generated by automaton in $\mathcal{C}$, of a result of Chou showing that finitely generated elementary amenable groups either have polynomial growth or contain a free semigroup of rank at least 2.

37pages; following a referee's comments, the contents of Section 7 have been made into a separate article, abstract has been amended accordingly

Cited by in corpus (3)

• The further chameleon groups of Richard Thompson and Graham Higman: Automorphisms via dynamics for the Higman groups $G_{n,r}$
• Automorphisms of shift spaces and the Higman--Thompson groups: the one-sided case
• The core growth of strongly synchronizing transducers