Regular left-orders on groups



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Antolín Pichel, Yago and Rivas, Cristóbal and Lu Su, Hang (2021) Regular left-orders on groups. (Unpublished)

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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.

Item Type:Article
Uncontrolled Keywords:Ordered groups; Formal languages; Baumslag-Solitar groups
Subjects:Sciences > Mathematics > Cybernetics
Sciences > Mathematics > Group Theory
ID Code:72936
Deposited On:20 Jun 2022 14:41
Last Modified:27 Jun 2022 09:49

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