A Connected 3-State Reversible Mealy Automaton Cannot Generate an Infinite Burnside Group

Conference paper

DOI: 10.1007/978-3-319-21500-6_25

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9168)
Cite this paper as:
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

Abstract

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.

Keywords

Burnside groups Reversible mealy automata Automaton groups 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Ines Klimann
    • 1
  • Matthieu Picantin
    • 1
  • Dmytro Savchuk
    • 2
  1. 1.University Paris Diderot, Sorbonne Paris Cité, LIAFA, UMR 7089 CNRSParisFrance
  2. 2.Department of Mathematics and StatisticsUniversity of South FloridaTampaUSA

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