On (bi)reversible automata generating lamplighter groups

Piotr W. Nowak; Andriy Oliynyk; Veronika Prokhorchuk

On (bi)reversible automata generating lamplighter groups

Group Theory 2023-08-14 v1

Authors: Piotr W. Nowak , Andriy Oliynyk , Veronika Prokhorchuk

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.

Keywords

wreath product of groups abelian groups

Cite

@article{arxiv.2308.05808,
  title  = {On (bi)reversible automata generating lamplighter groups},
  author = {Piotr W. Nowak and Andriy Oliynyk and Veronika Prokhorchuk},
  journal= {arXiv preprint arXiv:2308.05808},
  year   = {2023}
}

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