English

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