Title

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

Document Type

Article

Publication Date

2018

Keywords

Burnside groups, reversible Mealy automata, automaton groups

Digital Object Identifier (DOI)

https://doi.org/10.1142/S0129054118400087

Abstract

The class of automaton groups is a rich source of the simplest examples of infinite Burnside groups. However, all such examples have been constructed as groups generated by non-reversible automata. Moreover, 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.

Was this content written or created while at USF?

Yes

Citation / Publisher Attribution

International Journal of Foundations of Computer Science, v. 29, issue 2, p. 297-314

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