Property FA is not a profinite property

2022/12/16 by Tamunonye Cheetham‐West, Cheetham-West, Tamunonye, Alexander Lubotzky +5
Mathematics · #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2212.08207

openalex publication_date 2022/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We exhibit infinitely many pairs of non-isomorphic finitely presented, residually finite groups Δ and Γ with Δ having Property FA, Γ having a non-trivial action on a tree and Δ and Γ having isomorphic profinite completions.

Related

• Finiteness Properties and Profinite Completions
• Profinite completions and Kazhdan's property (T)
• The strong profinite genus of a finitely presented group can be infinite
• Absolute profinite rigidity, direct products, and finite presentability
• Constructing uncountably many groups with the same profinite completion