%0 Journal Article
%A Antolín Pichel, Yago
%A Rivas, Cristóbal
%A Lu Su, Hang
%T Regular left-orders on groups
%D 2021
%U https://hdl.handle.net/20.500.14352/7213
%X A 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.
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