Star-free geodesic languages for groups
Group Theory
2011-11-04 v1
Abstract
In this article we show that every group with a finite presentation satisfying one or both of the small cancellation conditions and has the property that the set of all geodesics (over the same generating set) is a star-free regular language. Star-free regularity of the geodesic set is shown to be dependent on the generating set chosen, even for free groups. We also show that the class of groups whose geodesic sets are star-free with respect to some generating set is closed under taking graph (and hence free and direct) products, and includes all virtually abelian groups.
Keywords
Cite
@article{arxiv.1111.0784,
title = {Star-free geodesic languages for groups},
author = {S. Hermiller and Derek F. Holt and Sarah Rees},
journal= {arXiv preprint arXiv:1111.0784},
year = {2011}
}