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The Lamplighter Group ℤ<sub>3</sub>≀ℤ Generated by a Bireversible Automaton
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.