Finiteness Properties and Profinite Completions

2012/11/28 by Lubotzky, Alexander
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1211.6573

Abstract

In this note we show that various (geometric/homological) finiteness properties are not profinite properties. For example for every 1 ≤ k, ℓ ≤ \bbn, there exist two finitely generated residually finite groups \Ga₁ and \Ga₂ with isomorphic profinite completions, such that \Ga₁ is strictly of type F_k and \Ga₂ of type F_ℓ.

Related

• Profinite completions and Kazhdan's property (T)
• Property FA is not a profinite property
• Finiteness properties of profinite groups
• Constructing uncountably many groups with the same profinite completion
• Amenability and profinite completions of finitely generated groups