The lamplighter group of rank two generated by a bireversible automaton

Elsayed Ahmed; Dmytro Savchuk

The lamplighter group of rank two generated by a bireversible automaton

Group Theory 2018-02-13 v1

Authors: Elsayed Ahmed , Dmytro Savchuk

Abstract

We construct a 4-state 2-letter bireversible automaton generating the lamplighter group $(\mathbb Z_2^2)\wr\mathbb Z$ of rank two. The action of the generators on the boundary of the tree can be induced by the affine transformations on the ring $\mathbb Z_2[[t]]$ of formal power series over $\mathbb Z_2$ .

Keywords

lamplighter group bireversible automaton rank two tree boundary affine transformations formal power series

Cite

@article{arxiv.1802.03695,
  title  = {The lamplighter group of rank two generated by a bireversible automaton},
  author = {Elsayed Ahmed and Dmytro Savchuk},
  journal= {arXiv preprint arXiv:1802.03695},
  year   = {2018}
}

Comments

18 pages, 2 figures

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