Free products of bi-orderable groups

2024/03/21 by Kyrylo Muliarchyk, Muliarchyk, Kyrylo · 1 citation
Mathematics · #05F15 #20F60 #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2403.14779

openalex publication_date 2024/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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(F₂) on F₂ does not have dense orbits.

Cited by

• Spaces of left-preorders on free products

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• Left-orderings on free products of groups
• On the topology of the space of bi-orderings of a free group on two generators
• Ordered bases, order-preserving automorphisms and bi-orderable link groups
• Topology of the space of bi-orderings of a free group on two generators
• Automorphisms acting on the left-orderings of a bi-orderable group