Realization of big centralizers of minimal aperiodic actions on the Cantor set
Autor: | Samuel Petite, María Isabel Cortez |
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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: |
Group (mathematics)
Computer Science::Information Retrieval Applied Mathematics [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] Mathematics::General Topology Residually finite group 01 natural sciences Centralizer and normalizer 010101 applied mathematics Combinatorics Cantor set Mathematics::Logic Aperiodic graph Free group Discrete Mathematics and Combinatorics Countable set 0101 mathematics Abelian group ComputingMilieux_MISCELLANEOUS Analysis Mathematics |
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 |
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