Tree languages and branched groups
Group Theory
2022-03-25 v1
Abstract
We study the portraits of isometries of rooted trees - the labelling of the tree, at each vertex, by the permutation of its descendants - in terms of languages. We characterize regularly branched self-similar groups in terms of -regular languages. We deduce the algorithmic decidability of some problems, such as the comparison of regularly branched contracting groups, and their orbit structure on the boundary of the rooted tree.
Keywords
Cite
@article{arxiv.2203.12963,
title = {Tree languages and branched groups},
author = {Laurent Bartholdi and Marialaura Noce},
journal= {arXiv preprint arXiv:2203.12963},
year = {2022}
}