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The lamplighter group \(\mathbb Z_3 \wr \mathbb Z\) generated by a bireversible automaton. (English) Zbl 1368.20033
Summary: We construct a bireversible self-dual automaton with three states over an alphabet with three letters which generates the lamplighter group \(\mathbb Z_3 \wr \mathbb Z\). In particular, this fact shows that not all groups defined by birevirsible automata are finitely presented.

MSC:
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
20E08 Groups acting on trees
20E22 Extensions, wreath products, and other compositions of groups
20F05 Generators, relations, and presentations of groups
68Q70 Algebraic theory of languages and automata
Software:
AutomGrp
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References:
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