Finite-state self-similar actions of nilpotent groups

Ievgen V. Bondarenko, Rostyslav V. Kravchenko

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Let G be a finitely generated torsion-free nilpotent group and φ : H → G be a surjective homomorphism from a subgroup H < G of finite index with trivial φ-core. For every choice of coset representatives of H in G there is a faithful self-similar action of the group G associated with (G, φ). We are interested in what cases all these actions are finite-state and in what cases there exists a finite-state self-similar action for (G, φ). These two properties are characterized in terms of the Jordan normal form of the corresponding automorphism̂φ of the Lie algebra of the Mal'cev completion of G.

Original languageEnglish (US)
Pages (from-to)339-348
Number of pages10
JournalGeometriae Dedicata
Volume163
Issue number1
DOIs
StatePublished - Apr 2013

Keywords

  • Automaton group
  • Finite-state action
  • Nilpotent group
  • Self-similar action

ASJC Scopus subject areas

  • Geometry and Topology

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