No positive cone in a free product is regular
Group Theory
2017-11-16 v2
Abstract
We show that there exists no left order on the free product of two nontrivial, finitely generated, left-orderable groups such that the corresponding positive cone is represented by a regular language. Since there are orders on free groups of rank at least two with positive cone languages that are context-free (in fact, 1-counter languages), our result provides a bound on the language complexity of positive cones in free products that is the best possible within the Chomsky hierarchy. It also provides a strengthening of a result by Cristobal Rivas stating that the positive cone in a free product of nontrivial, finitely generated, left-orderable groups cannot be finitely generated as a semigroup.
Keywords
Cite
@article{arxiv.1609.06288,
title = {No positive cone in a free product is regular},
author = {Susan Hermiller and Zoran Sunic},
journal= {arXiv preprint arXiv:1609.06288},
year = {2017}
}
Comments
8 pages