2016/04/12 by Thibault Godin, Godin, Thibault, Ines Klimann +1
Mathematics · #20E08 #20F65 #68Q45 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #F.1.1 #F.4.3 #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #G.2.M #Geometric and Algebraic Topology #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.1604.03270
openalex publication_date 2016/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.