Finite automata of polynomial growth do not generate a free group.
In an earlier paper, the author conjectured that finite-state automata of polynomial growth cannot generate free groups of rank 2. In this paper, the author proves, under some natural hypotheses, that finite-state automorphisms of polynomial growth cannot generate free subgroups of rank 2 of the group of automorphisms of a regular rooted tree of arbitrary degree.
scientific article; zbMATH DE number 2145817