Lamplighter groups and automata


Jain S., Moldagaliyev B., Stephan F., Tien Dat Tran T. D. T.

ACTA INFORMATICA, 2022 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2022
  • Doi Number: 10.1007/s00236-022-00423-3
  • Title of Journal : ACTA INFORMATICA

Abstract

This paper investigates presentations of lamplighter groups using computationalmodels from automata theory. The present work shows that if G can be presented such that the full group operation is recognised by a transducer, then the same is true for the lamplighter group G (sic) Z of G. Furthermore, Cayley presentations, where only multiplications with constants are recognised by transducers, are used to study generalised lamplighter groups of the form G (sic) Zd and G (sic) Fd, where Fd is the free group over d generators. Additionally, Zk (sic) Z2 and Zk (sic) Fd are shown to be Cayley tree automatic.