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arXiv · 1807.04654

On the centralizers of minimal aperiodic actions on the Cantor set

Maria Isabel Cortez·Samuel Petite
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Abstract

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 $\mathbb Z$ 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 $G$, the centralizer of any minimal aperiodic $G$-action on the Cantor set is a subgroup of the centralizer of a minimal $\mathbb Z$-action.

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Maria Isabel Cortez, Samuel Petite. 2018-07-12. On the centralizers of minimal aperiodic actions on the Cantor set. https://arxiv.org/abs/1807.04654

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