Geodesic
The isomorphism problem for profinite completions of finitely presented, residually finite groups
Martin R. Bridson1 orcid ; Henry Wilton2
1University of Oxford, UK
2University of Cambridge, Great Britain
Groups, geometry, and dynamics, Tome 8 (2014) no. 3, pp. 733-745

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DOI

We consider pairs of finitely presented, residually finite groups u:P↪Γ. We prove that there is no algorithm that, given an arbitrary such pair, can determine whether or not the associated map of profinite completions u^:P→Γ is an isomorphism. Nor do there exist algorithms that can decide whether u^ is surjective, or whether P is isomorphic to Γ.
DOI : 10.4171/ggd/245
Classification : 20-XX
Mots-clés : Profinite completions, residually finite groups, finitely presented groups, decision problems

Martin R. Bridson  1   ; Henry Wilton  2

1 University of Oxford, UK
2 University of Cambridge, Great Britain 
Martin R. Bridson; Henry Wilton. The isomorphism problem for profinite completions of finitely presented, residually finite groups. Groups, geometry, and dynamics, Tome 8 (2014) no. 3, pp. 733-745. doi: 10.4171/ggd/245
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