2021/04/09 by Yago Antolín, Antolín, Yago, Cristóbal Rivas +4
Computer Science · Mathematics · #06F15 #20F60 #68Q45 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #math.GR #msc:06F15 #msc:20F60 #msc:68Q45 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2104.04475
v2: 43 pages,9 figures. Exposition improved. Construction of Theorem 5.14 simplified
openalex publication_date 2021/04/09 · arxiv created 2021/09/17 · arxiv updated 2021/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A regular left-order on finitely generated group G is a total, left-multiplication invariant order on G 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 give a classification of the groups all whose left-orders are regular left-orders. In addition, we prove that solvable Baumslag-Solitar groups B(1,n) admits a regular left-order if and only if n≥ -1. Finally, Hermiller and Sunic showed that no free product admits a regular left-order, however we show that if A and B are groups with regular left-orders, then (A*B)× ℤ admits a regular left-order.