The lamplighter group of rank two generated by a bireversible automaton
Elsayed Ahmed, Dmytro Savchuk · Communications in Algebra · 2019
We construct a 4-state 2-letter bireversible automaton generating the lamplighter group (ℤ22)≀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 ℤ2[[t]] of formal power series over ℤ2.