The lamplighter group of rank two generated by a bireversible automaton

2018/02/11 by Elsayed Ahmed, Ahmed, Elsayed, Dmytro Savchuk +1
Mathematics · #20E08 #20F65 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20E08 #msc:20F65

paper · pdf · doi:10.48550/arxiv.1802.03695

18 pages, 2 figures

arxiv created 2018/02/11 · arxiv updated 2018/02/13

Abstract

We construct a 4-state 2-letter bireversible automaton generating the lamplighter group (\mathbb Z₂²)\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 Z₂[[t]] of formal power series over \mathbb Z₂.

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