Finiteness properties and profinite completions

Alexander Lubotzky

doi:10.1112/blms/bdt070

Finiteness properties and profinite completions

Alexander Lubotzky^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

In this note, we show that various (geometric/homological) finiteness properties are not profinite properties. For example, for all positive integers k and ℓ, there exist two finitely generated residually finite groups Γ₁ and Γ₂ with isomorphic profinite completions, such that Γ₁ is strictly of type F_k and Γ₂ of type F_ℓ.

Original language	English
Pages (from-to)	103-110
Number of pages	8
Journal	Bulletin of the London Mathematical Society
Volume	46
Issue number	1
DOIs	https://doi.org/10.1112/blms/bdt070
State	Published - Feb 2014

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AB - In this note, we show that various (geometric/homological) finiteness properties are not profinite properties. For example, for all positive integers k and ℓ, there exist two finitely generated residually finite groups Γ1 and Γ2 with isomorphic profinite completions, such that Γ1 is strictly of type Fk and Γ2 of type Fℓ.

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Finiteness properties and profinite completions

Abstract

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