Mathematics, Department of
Department of Mathematics: Faculty Publications
Accessibility Remediation
If you are unable to use this item in its current form due to accessibility barriers, you may request remediation through our remediation request form.
Document Type
Article
Date of this Version
2017
Citation
Vol. 27, No. 8 (2017) 1113–1120
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 which states that the positive cone in a free product of nontrivial, finitely generated, left-orderable groups cannot be finitely generated as a semigroup. As another illustration of our method, we show that the language of all geodesics (with respect to the natural generating set) that represent positive elements in a graph product of groups defined by a graph of diameter at least 3 cannot be regular.
Comments
Copyright World Scientific Publishing Company
DOI: 10.1142/S0218196717500527