For every non-trivial finite abelian group A$A$, we exhibit a bireversible automaton generating the lamplighter group A wreath product Z$A \wr \mathbb {Z}$.
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Ohio State Univ, Dept Math, Math Tower 414,231 W 18th Ave, Columbus, OH 43210 USAOhio State Univ, Dept Math, Math Tower 414,231 W 18th Ave, Columbus, OH 43210 USA
Skipper, Rachel
Steinberg, Benjamin
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CUNY City Coll, Dept Math, NAC 8-133,Convent Ave & 138th St, New York, NY 10031 USAOhio State Univ, Dept Math, Math Tower 414,231 W 18th Ave, Columbus, OH 43210 USA
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Univ Paris Diderot, Sorbonne Paris Cite, CNRS, IRIF,UMR 8243, F-75013 Paris, FranceUniv Paris Diderot, Sorbonne Paris Cite, CNRS, IRIF,UMR 8243, F-75013 Paris, France
Godin, Thibault
Klimann, Ines
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Univ Paris Diderot, Sorbonne Paris Cite, CNRS, IRIF,UMR 8243, F-75013 Paris, FranceUniv Paris Diderot, Sorbonne Paris Cite, CNRS, IRIF,UMR 8243, F-75013 Paris, France