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
Scholar Commons Citation
Ahmed, Elsayed and Savchuk, Dmytro, "The Lamplighter Group of Rank Two Generated by a Bireversible Automaton" (2019). Mathematics and Statistics Faculty Publications. 141.
https://digitalcommons.usf.edu/mth_facpub/141
