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arXiv · 1212.0605

Self-similar groups acting essentially freely on the boundary of the binary rooted tree

Rostislav Grigorchuk·Dmytro Savchuk
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Abstract

We study the class of groups generated by automata that act essentially freely on the boundary of a rooted tree. In the process we establish and discuss some general tools for determining if a group belongs to this class, and explore the connections of this class to the classes of just-infinite and scale-invariant groups. Our main application is a complete classification of groups generated by 3-state automata over 2-letter alphabet that are in this class.

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Rostislav Grigorchuk, Dmytro Savchuk. 2013-08-12. Self-similar groups acting essentially freely on the boundary of the binary rooted tree. https://arxiv.org/abs/1212.0605

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