Connected reversible Mealy automata of prime size cannot generate infinite Burnside groups
Formal Languages and Automata Theory
2016-04-13 v1 Group Theory
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.
Keywords
Cite
@article{arxiv.1604.03270,
title = {Connected reversible Mealy automata of prime size cannot generate infinite Burnside groups},
author = {Thibault Godin and Ines Klimann},
journal= {arXiv preprint arXiv:1604.03270},
year = {2016}
}
Comments
arXiv admin note: text overlap with arXiv:1409.6142