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arXiv · 2403.14779

Free products of bi-orderable groups

Kyrylo Muliarchyk
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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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Kyrylo Muliarchyk. 2024-03-21. Free products of bi-orderable groups. https://arxiv.org/abs/2403.14779

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