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arXiv · 2308.05808

On (bi)reversible automata generating lamplighter groups

Piotr W. Nowak·Andriy Oliynyk·Veronika Prokhorchuk
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Abstract

For any nontrivial abelian group $\mathbb{X}$ we construct a reversible (bireversible in case the order of $\mathbb{X}$ is odd) automaton such that its set of states and alphabet are identified with $\mathbb{X}$, transition and output functions are defined via the left and the right regular actions correspondingly and its group splits into the restricted wreath product $\mathbb{X} \wr \mathbb{Z}$, i.e. is a lamplighter group.

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Piotr W. Nowak, Andriy Oliynyk, Veronika Prokhorchuk. 2023-08-10. On (bi)reversible automata generating lamplighter groups. https://arxiv.org/abs/2308.05808

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