Geodesic
Property FA is not a profinite property
Tamunonye Cheetham-West1 orcid ; Alexander Lubotzky2 orcid ; Alan W. Reid3 orcid ; Ryan Spitler3
1Yale University, New Haven, USA
2Weizmann Institute of Science, Rehovot, Israel
3Rice University, Houston, USA
Groups, geometry, and dynamics, Tome 19 (2025) no. 3, pp. 1081-1087

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DOI

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.
DOI : 10.4171/ggd/802
Classification : 20E18, 20E06
Mots-clés : profinite property, Property FA, profinite rigidity, S-arithmetic

Tamunonye Cheetham-West  1   ; Alexander Lubotzky  2   ; Alan W. Reid  3   ; Ryan Spitler  3

1 Yale University, New Haven, USA
2 Weizmann Institute of Science, Rehovot, Israel
3 Rice University, Houston, USA 
Tamunonye Cheetham-West; Alexander Lubotzky; Alan W. Reid; Ryan Spitler. Property FA is not a profinite property. Groups, geometry, and dynamics, Tome 19 (2025) no. 3, pp. 1081-1087. doi: 10.4171/ggd/802
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     title = {Property {FA} is not a profinite property},
     journal = {Groups, geometry, and dynamics},
     pages = {1081--1087},
     year = {2025},
     volume = {19},
     number = {3},
     doi = {10.4171/ggd/802},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/802/}
}
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