Connected reversible Mealy automata of prime size cannot generate infinite Burnside groups. (English) Zbl 1398.68309
Faliszewski, Piotr (ed.) et al., 41st international symposium on mathematical foundations of computer science, MFCS 2016, Kraków, Poland, August 22–26, 2016. Proceedings. Wadern: Schloss Dagstuhl – Leibniz Zentrum für Informatik (ISBN 978-3-95977-016-3). LIPIcs – Leibniz International Proceedings in Informatics 58, Article 44, 14 p. (2016).
Summary: 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.
For the entire collection see [Zbl 1351.68015].
For the entire collection see [Zbl 1351.68015].
MSC:
| 68Q45 | Formal languages and automata |
| 20F10 | Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) |
| 20F50 | Periodic groups; locally finite groups |
| 68Q70 | Algebraic theory of languages and automata |
