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

2012/12/04 by Grigorchuk, Rostislav, Savchuk, Dmytro
#20F65 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1212.0605

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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