The Lamplighter Group ℤ3≀ℤ Generated by a Bireversible Automaton

DOI10.1080/00927872.2016.1172602zbMath1368.20033arXiv1502.07981OpenAlexW2407554820MaRDI QIDQ2827247

Emanuele Rodaro, Ievgen V. Bondarenko, Daniele D'Angeli

Publication date: 12 October 2016

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.07981

zbMATH Keywords

lamplighter groupautomaton groupbireversible automaton

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Algebraic theory of languages and automata (68Q70) Extensions, wreath products, and other compositions of groups (20E22) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Groups acting on trees (20E08)

Related Items (9)

Freeness of automaton groups vs boundary dynamics ⋮ Affine automorphisms of rooted trees ⋮ Automaton groups and complete square complexes ⋮ On groups generated by bi-reversible automata: the two-state case over a changing alphabet ⋮ Bireversible automata generating lamplighter groups ⋮ On state-closed representations of restricted wreath product of groups \(G_{p,d}=C_{p}wrC^{d}\) ⋮ The lamplighter group of rank two generated by a bireversible automaton ⋮ Boundary dynamics for bireversible and for contracting automaton groups ⋮ Lamplighter groups, bireversible automata, and rational series over finite rings

Uses Software

• AutomGrp

Cites Work

• Affine automorphisms of rooted trees
• Automata generating free products of groups of order 2.
• On a series of finite automata defining free transformation groups.
• Automata and square complexes.
• On a question of Atiyah
• Groups and semigroups defined by colorings of synchronizing automata
• On the lattice of subgroups of the lamplighter group
• AUTOMATA OVER A BINARY ALPHABET GENERATING FREE GROUPS OF EVEN RANK
• ON A CLASS OF AUTOMATA GROUPS GENERALIZING LAMPLIGHTER GROUPS
• The lamplighter group as a group generated by a 2-state automaton, and its spectrum

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