Finitely constrained groups of maximal Hausdorff dimension
Group Theory
2015-12-30 v2
Abstract
We prove that if G_P is a finitely constrained group of binary rooted tree automorphisms (a group binary tree subshift of finite type) defined by an essential pattern group P of pattern size d, d>1, and if G_P has maximal Hausdorff dimension (equal to 1-1/2^{d-1}), then G_P is not topologically finitely generated. We describe precisely all essential pattern groups P that yield finitely constrained groups with maximal Haudorff dimension. For a given size d, d>1, there are exactly 2^{d-1} such pattern groups and they are all maximal in the group of automorphisms of the finite rooted regular tree of depth d.
Keywords
Cite
@article{arxiv.1406.0522,
title = {Finitely constrained groups of maximal Hausdorff dimension},
author = {Andrew Penland and Zoran Sunic},
journal= {arXiv preprint arXiv:1406.0522},
year = {2015}
}