2000 character limit reached
Connected reversible Mealy automata of prime size cannot generate infinite Burnside groups (1604.03270v1)
Published 12 Apr 2016 in cs.FL and math.GR
Abstract: The simplest example of an infinite Burnside group arises in the class of automaton groups. However there is no known example of such a group generated by a reversible Mealy automaton. It has been proved that, for a connected automaton of size at most~3, or when the automaton is not bireversible, the generated group cannot be Burnside infinite. In this paper, we extend these results to automata with bigger stateset, proving that, if a connected reversible automaton has a prime number of states, it cannot generate an infinite Burnside group.