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Free products of bi-orderable groups

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arxiv 2403.14779 v1 pith:VKH6JABN submitted 2024-03-21 math.GR

Kyrylo Muliarchyk This is my paper · ORCID
classification math.GR
keywords groupsbi-orderedfreeproductsactionadmitautomorphismbi-orderable
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abstract

We prove a bi-ordered version of Rivas' result for free products of left-order groups. Namely, we show that a free product of bi-ordered groups does not admit isolated bi-ordering. Our method relies on the dynamical realization of bi-ordered groups. We also show that the natural action of the automorphism group $Aut(F_2)$ on $F_2$ does not have dense orbits.

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  1. Spaces of left-preorders on free products

    math.GR 2025-07 conditional novelty 6.0 of 10

    Left-preorder spaces of free products have no isolated elements; when the factors are finitely generated, every nonempty such space is a Cantor set.

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