The Lamplighter Group ℤ3≀ℤ Generated by a Bireversible Automaton
Ievgen Bondarenko, Daniele D’Angeli, Emanuele Rodaro · Communications in Algebra · 2016
We construct a bireversible self-dual automaton with three states over an alphabet with three letters which generates the lamplighter group ℤ3≀ℤ. In particular, this fact shows that not all groups defined by birevirsible automata are finitely presented.