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arXiv · 2606.13838

Free product of bi-orderable group is bi-orderable: A simple dynamical proof

Juan Alonso·Cristóbal Rivas
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Abstract

We give a new proof of Vinogradov's theorem asserting that free product of biorderable groups is biorderable. Our proof relies on a simple dynamical construction that provides a bi-ordering of the free product that extends the bi-orderings on the factors. Furthermore, if the bi-orders of the factors are invariant under some automorphisms, then the bi-ordering on the product turns out to be invariant under the product automorphism.

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Juan Alonso, Cristóbal Rivas. 2026-06-11. Free product of bi-orderable group is bi-orderable: A simple dynamical proof. https://arxiv.org/abs/2606.13838

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