Lamplighter groups and automata
Jain S. Moldagaliyev B. Stephan F. Tran T.D.
August 2022Springer Science and Business Media Deutschland GmbH
Acta Informatica
2022#59Issue 4451 - 478 pp.
This paper investigates presentations of lamplighter groups using computational models 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≀ 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≀ Zd and G≀ Fd, where Fd is the free group over d generators. Additionally, Zk≀ Z2 and Zk≀ Fd are shown to be Cayley tree automatic.
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School of Computing, National University of Singapore, Singapore, 117417, Singapore
Suleyman Demirel University, 1/1 Abylai Khan Street, Almaty, Kaskelen, 040900, Kazakhstan
Department of Mathematics, National University of Singapore, Singapore, 119076, Singapore
School of Computing
Suleyman Demirel University
Department of Mathematics
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