Property FA is not a profinite property

Tamunonye Cheetham-West; Alexander Lubotzky; Alan W. Reid; Ryan Spitler

doi:10.4171/GGD/802

Property FA is not a profinite property

Tamunonye Cheetham-West
, Alexander Lubotzky
, Alan W. Reid
, Ryan Spitler

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

2 Scopus citations

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.

Original language	English
Pages (from-to)	1081-1087
Number of pages	7
Journal	Groups, Geometry, and Dynamics
Volume	19
Issue number	3
DOIs	https://doi.org/10.4171/GGD/802
State	Published - 2025
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2024 European Mathematical Society.

Keywords

Property FA
S-arithmetic
profinite property
profinite rigidity

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10.4171/GGD/802

Cite this

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title = "Property FA is not a profinite property",

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.",

keywords = "Property FA, S-arithmetic, profinite property, profinite rigidity",

author = "Tamunonye Cheetham-West and Alexander Lubotzky and Reid, \{Alan W.\} and Ryan Spitler",

note = "Publisher Copyright: {\textcopyright} 2024 European Mathematical Society.",

year = "2025",

doi = "10.4171/GGD/802",

language = "אנגלית",

volume = "19",

pages = "1081--1087",

journal = "Groups, Geometry, and Dynamics",

issn = "1661-7207",

publisher = "European Mathematical Society Publishing House",

number = "3",

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T1 - Property FA is not a profinite property

AU - Cheetham-West, Tamunonye

AU - Lubotzky, Alexander

AU - Reid, Alan W.

AU - Spitler, Ryan

PY - 2025

Y1 - 2025

N2 - 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.

AB - 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.

KW - Property FA

KW - S-arithmetic

KW - profinite property

KW - profinite rigidity

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DO - 10.4171/GGD/802

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AN - SCOPUS:105015085515

SN - 1661-7207

VL - 19

SP - 1081

EP - 1087

JO - Groups, Geometry, and Dynamics

JF - Groups, Geometry, and Dynamics

IS - 3

ER -

Property FA is not a profinite property

Abstract

Bibliographical note

Keywords

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