arXiv · 2202.04107
We are following [4]. Nevertheless we are interested only in claryfication that the lamplighter group can be realized as a 2--states Mealy machine.
Jānis Buls. 2022-02-05. The Lamplighter Group. https://arxiv.org/abs/2202.04107
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We investigate reversible elements in the Picard modular group $\mathrm{PSL}(2,\mathbb{Z}[i])$. We show that reversibility coincides with strong reversibility for Kleinian groups, in particular for the Picard group. We classify reversible elements in the Picard group and characterize loxodromic reversible elements up to conjugacy. We prove that each such conjugacy class contains exactly eight special representatives. We also obtain asymptotic estimates for the number of reversible conjugacy classes with bounded trace.
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