The lamplighter group ℤ3≀ℤ generated by a bireversible automaton

Daniele D'Angeli; Ievgen Bondarenko; Emanuele Rodaro

doi:10.1080/00927872.2016.1172602

The lamplighter group ℤ3≀ℤ generated by a bireversible automaton

Daniele D'Angeli^*, Ievgen Bondarenko, Emanuele Rodaro

^*Corresponding author for this work

Institute of Discrete Mathematics (5050)

Research output: Contribution to journal › Article › peer-review

Abstract

We construct a bireversible self-dual automaton with three states over an alphabet with three letters which generates the lamplighter group ℤ3≀ℤ. In particular, this fact shows that not all groups defined by birevirsible automata are finitely presented.

Original language	English
Pages (from-to)	5257-5268
Journal	Communications in Algebra
Volume	44
Issue number	12
DOIs	https://doi.org/10.1080/00927872.2016.1172602
Publication status	Published - 2016

Fields of Expertise

Information, Communication & Computing

Treatment code (Nähere Zuordnung)

Theoretical

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10.1080/00927872.2016.1172602

Cite this

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title = "The lamplighter group ℤ3≀ℤ generated by a bireversible automaton",

abstract = "We construct a bireversible self-dual automaton with three states over an alphabet with three letters which generates the lamplighter group ℤ3≀ℤ. In particular, this fact shows that not all groups defined by birevirsible automata are finitely presented.",

author = "Daniele D'Angeli and Ievgen Bondarenko and Emanuele Rodaro",

year = "2016",

doi = "10.1080/00927872.2016.1172602",

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AU - Bondarenko, Ievgen

AU - Rodaro, Emanuele

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Y1 - 2016

N2 - We construct a bireversible self-dual automaton with three states over an alphabet with three letters which generates the lamplighter group ℤ3≀ℤ. In particular, this fact shows that not all groups defined by birevirsible automata are finitely presented.

AB - We construct a bireversible self-dual automaton with three states over an alphabet with three letters which generates the lamplighter group ℤ3≀ℤ. In particular, this fact shows that not all groups defined by birevirsible automata are finitely presented.

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DO - 10.1080/00927872.2016.1172602

M3 - Article

SN - 1532-4125

VL - 44

SP - 5257

EP - 5268

JO - Communications in Algebra

JF - Communications in Algebra

IS - 12

ER -

The lamplighter group ℤ3≀ℤ generated by a bireversible automaton

Abstract

Fields of Expertise

Treatment code (Nähere Zuordnung)

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Cite this