The lamplighter group L(h)n
This paper discusses a finite group associated to a machine called a lamplighter, having n lamps with h settings arranged in a circle around a single lighter. The properties of the group are discussed. Criteria for determining whether group elements are conjugates, commutators or in the center are established.
Mamaril, M. C. C., & De Las Peñas, M. L. A. N. (2016, February). The lamplighter group L n (h). In AIP Conference Proceedings (Vol. 1707, No. 1, p. 020011). AIP Publishing LLC.