Geodesic
The strong profinite genus of a finitely presented group can be infinite
Journal of the European Mathematical Society, Tome 18 (2016) no. 9, pp. 1909-1918

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We construct the first examples of finitely-presented, residually-finite groups Γ that contain an infinite sequence of non-isomorphic finitely-presented subgroups Pn​↪Γ such that the inclusion maps induce isomorphisms of profinite completions Pn​≅Γ.
DOI : 10.4171/jems/633
Classification : 20-XX
Keywords: Profinite completion, profinite genus, Grothendieck pairs 
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     author = {Martin R. Bridson},
     title = {The strong profinite genus of a finitely presented group can be infinite},
     journal = {Journal of the European Mathematical Society},
     pages = {1909--1918},
     publisher = {mathdoc},
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     number = {9},
     year = {2016},
     doi = {10.4171/jems/633},
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}
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Martin R. Bridson. The strong profinite genus of a finitely presented group can be infinite. Journal of the European Mathematical Society, Tome 18 (2016) no. 9, pp. 1909-1918. doi: 10.4171/jems/633

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