  The class of automaton groups is a rich source of the simplest examples of
infinite Burnside groups. However, there are some classes of automata that do
not contain such examples. For instance, all infinite Burnside automaton groups
in the literature are generated by non reversible Mealy automata and it was
recently shown that 2-state invertible-reversible Mealy automata cannot
generate infinite Burnside groups. Here we extend this result to connected
3-state invertible-reversible Mealy automata, using new original techniques.
The results provide the first uniform method to construct elements of infinite
order in each infinite group in this class.
