Freeness of Sch\"utzenberger groups of primitive substitutions
Group Theory
2022-12-20 v1
Abstract
Our main goal is to study the freeness of Sch\"utzenberger groups defined by primitive substitutions. Our findings include a simple freeness test for these groups, which is applied to exhibit a primitive invertible substitution with corresponding non-free Sch\"utzenberger group. This constitutes a counterexample to a result of Almeida dating back to 2005. We also give some early results concerning relative freeness of Sch\"utzenberger groups, a question which remains largely unexplored.
Keywords
Cite
@article{arxiv.2109.11957,
title = {Freeness of Sch\"utzenberger groups of primitive substitutions},
author = {Herman Goulet-Ouellet},
journal= {arXiv preprint arXiv:2109.11957},
year = {2022}
}