Journal article
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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(Preview, Accepted manuscript, pdf, 181.5KB, Terms of use)
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- Publisher copy:
- 10.4171/GGD/245
Authors
+ Engineering and Physical Sciences Research Council
More from this funder
- Funding agency for:
- Bridson, M
- Publisher:
- European Mathematical Society
- Journal:
- Groups, Geometry, and Dynamics More from this journal
- Volume:
- 8
- Issue:
- 3
- Pages:
- 733–745
- Publication date:
- 2014-01-01
- DOI:
- Keywords:
- Pubs id:
-
pubs:447407
- UUID:
-
uuid:888b0dd6-34c0-4e40-b185-0af4e85e1835
- Local pid:
-
pubs:447407
- Source identifiers:
-
447407
- Deposit date:
-
2016-10-20
Terms of use
- Copyright holder:
- European Mathematical Society
- Copyright date:
- 2014
- Notes:
- © European Mathematical Society
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