The lamplighter group $\mathbb{Z}_3\wr\mathbb{Z}$ generated by a bireversible automaton
نویسندگان
چکیده
We construct a bireversible self-dual automaton with 3 states over an alphabet with 3 letters which generates the lamplighter group Z3 ≀ Z. 2010 Mathematics Subject Classification: 20F65, 20M35
منابع مشابه
On a Class of Automata Groups Generalizing Lamplighter Groups
We study automata groups generated by reset automata. Every lamplighter group Z/nZ wr Z can be generated by such an automaton, and in general these automata groups are similar in nature to lamplighters: they are amenable locally-finite-by-cyclic groups; under mild decidable conditions, the semigroups generated by such automata are free. Parabolic subgroups and fractal properties are considered.
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