Antolín Pichel, YagoRivas, CristóbalLu Su, Hang2023-06-172023-06-172021-04-12https://hdl.handle.net/20.500.14352/7213A regular left-order on finitely generated group a 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.engjournal articleopen access512.54Ordered groupsFormal languagesBaumslag-Solitar groupsCibernética matemáticaGrupos (Matemáticas)1207.03 Cibernética