A Connected 3-State Reversible Mealy Automaton Cannot Generate an Infinite Burnside Group
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- Klimann I., Picantin M., Savchuk D. (2015) A Connected 3-State Reversible Mealy Automaton Cannot Generate an Infinite Burnside Group. In: Potapov I. (eds) Developments in Language Theory. DLT 2015. Lecture Notes in Computer Science, vol 9168. Springer, Cham
The class of automaton groups is a rich source of the simplest examples of infinite Burnside groups. However, no such examples have been constructed in some classes, as groups generated by non reversible automata. It was recently shown that 2-state reversible Mealy automata cannot generate infinite Burnside groups. Here we extend this result to connected 3-state reversible Mealy automata, using new original techniques. The results rely on a fine analysis of associated orbit trees and a new characterization of the existence of elements of infinite order.
KeywordsBurnside groups Reversible mealy automata Automaton groups
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