Pattern closure of groups of tree automorphisms
Group Theory
2010-12-10 v2
Abstract
It is shown that a group defined by forbidding all patterns of size s+1 that do not appear in a given self-similar group of tree automorphisms is the topological closure of a self-similar, countable, regular branch group, branching over its level s stabilizer. As an application, it is shown that there are no infinite, finitely constrained, topologically finitely generated groups of binary tree automorphisms defined by forbidden patterns of size two.
Cite
@article{arxiv.1012.1688,
title = {Pattern closure of groups of tree automorphisms},
author = {Zoran Sunic},
journal= {arXiv preprint arXiv:1012.1688},
year = {2010}
}