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The isomorphism problem for profinite completions of residually finite groups

Abstract:
We consider pairs of finitely presented, residually finite groups $u:P\hookrightarrow \Gamma$. We prove that there is no algorithm that, given an arbitrary such pair, can determine whether or not the associated map of profinite completions $\hat{u}: \widehat{P} \to \widehat{\Gamma}$ is an isomorphism. Nor do there exist algorithms that can decide whether $\hat{u}$ is surjective, or whether $\widehat{P}$ is isomorphic to $\widehat{\Gamma}$..
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.4171/GGD/245

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
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Funding agency for:
Bridson, M
Engineering and Physical Sciences Research Council More from this funder
Publisher:
European Mathematical Society Publisher's website
Journal:
Groups, Geometry, and Dynamics Journal website
Volume:
8
Issue:
3
Pages:
733–745
Publication date:
2014-01-01
DOI:
Source identifiers:
447407
Keywords:
Pubs id:
pubs:447407
UUID:
uuid:888b0dd6-34c0-4e40-b185-0af4e85e1835
Local pid:
pubs:447407
Deposit date:
2016-10-20

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