Title

The Lamplighter Group of Rank Two Generated by a Bireversible Automaton

Document Type

Article

Publication Date

2019

Keywords

Affine automorphism; automaton group; bireversible automaton; lamplighter group, 20E08, 20F65

Digital Object Identifier (DOI)

https://doi.org/10.1080/00927872.2018.1559322

Abstract

We construct a 4-state 2-letter bireversible automaton generating the lamplighter group (ℤ22)≀ℤ'>(Z22)≀Z(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]]'>Z2[[t]]ℤ2[[t]] of formal power series over ℤ2'>Z2ℤ2.

Was this content written or created while at USF?

Yes

Citation / Publisher Attribution

Communications in Algebra, v. 47, issue 8, p. 3340-3354

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