Regular left-orders on groups

Journal of Combinatorial Algebra

article

Yago Antolín¹  Cristóbal Rivas²  Hang Lu Su³ 

[1] Universidad Complutense de Madrid;Universidad de Chile;ICMAT

关键词: Left-orderable group;    regular language;    positive cone;    free products;    Baumslag–Solitar groups;    Tararin groups;   

DOI  :  10.4171/jca/64

学科分类：外科医学

来源: European Mathematical Society

【 摘 要 】

A regular left-order on a finitely generated group GGG is a total, left-multiplication invariant order on GGG whose corresponding positive cone is the image of a regular language over the generating set of the group under the evaluation map. We show that admitting regular left-orders is stable under extensions and wreath products and we give a classification of the groups whose left-orders are all regular left-orders. In addition, we prove that a solvable Baumslag–Solitar group B(1,n)B(1,n)B(1,n) admits a regular left-order if and only if n≥−1n\geq -1n≥−1. Finally, Hermiller and Šunić showed that no free product admits a regular left-order. We show that if AAA and BBB are groups with regular left-orders, then (A∗B)×Z(A*B)\times \mathbb{Z}(A∗B)×Z admits a regular left-order.

【 授权许可】

CC BY