Self-similar groups acting essentially freely on the boundary of the binary rooted tree
Group Theory
2013-08-13 v2
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.
Keywords
Cite
@article{arxiv.1212.0605,
title = {Self-similar groups acting essentially freely on the boundary of the binary rooted tree},
author = {Rostislav Grigorchuk and Dmytro Savchuk},
journal= {arXiv preprint arXiv:1212.0605},
year = {2013}
}
Comments
41 pages, 3 figures; final version: referee suggestions incorporated; to appear in Contemporary Mathematics