2019/05/30 by Hang Lu Su, Su, Hang Lu
Mathematics · #20F60 #68Q45 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20F60 #msc:68Q45
paper · pdf · doi:10.48550/arxiv.1905.13001
17 pages
arxiv created 2020/04/25 · arxiv updated 2020/04/28
We propose a criterion for preserving the regularity of a formal language representation when passing from groups to subgroups. We use this criterion to show that the regularity of a positive cone language in a left-orderable group passes to its finite index subgroups, and to show that there exists no left order on a finitely generated acylindrically hyperbolic group such that the corresponding positive cone is represented by a quasi-geodesic regular language. We also answer one of Navas' questions by giving an example of an infinite family of groups which admit a positive cone that is generated by exactly k generators, for every k ≥ 3. As a special case of our construction, we obtain a finitely generated positive cone for F2 × ℤ.