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Pré-Publication, Document De Travail Année : 2016

Connected reversible Mealy automata of prime size cannot generate infinite Burnside groups

Résumé

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.
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Dates et versions

hal-01296590 , version 1 (07-04-2016)
hal-01296590 , version 2 (31-08-2016)

Identifiants

Citer

Thibault Godin, Ines Klimann. Connected reversible Mealy automata of prime size cannot generate infinite Burnside groups. 2016. ⟨hal-01296590v1⟩
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