Realization of big centralizers of minimal aperiodic actions on the Cantor set

Autor: Samuel Petite, María Isabel Cortez
Přispěvatelé: Departamento de Matemática y Ciencia de la Computación [Santiago de Chile] (DMCC), Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352 (LAMFA), Université de Picardie Jules Verne (UPJV)-Centre National de la Recherche Scientifique (CNRS)
Rok vydání: 2020
Předmět:
Zdroj: Discrete & Continuous Dynamical Systems-A
Discrete & Continuous Dynamical Systems-A, 2020, 40 (5), pp.2891-2901. ⟨10.3934/dcds.2020153⟩
ISSN: 1553-5231
DOI: 10.3934/dcds.2020153
Popis: In this article we study the centralizer of a minimal aperiodic action of a countable group on the Cantor set (an aperiodic minimal Cantor system). We show that any countable residually finite group is the subgroup of the centralizer of some minimal \begin{document}$ \mathbb Z $\end{document} action on the Cantor set, and that any countable group is the subgroup of the normalizer of a minimal aperiodic action of an abelian countable free group on the Cantor set. On the other hand we show that for any countable group \begin{document}$ G $\end{document} , the centralizer of any minimal aperiodic \begin{document}$ G $\end{document} -action on the Cantor set is a subgroup of the centralizer of a minimal \begin{document}$ \mathbb Z $\end{document} -action.
Databáze: OpenAIRE