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Preprint Number 676

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676. Martin R. Bridson and Henry Wilton
The isomorphism problem for profinite completions of residually finite groups
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Submission date: 13 January 2014

Abstract:

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 \hat u: \hat P --> \hat Γ is an isomorphism. Nor do there exist algorithms that can decide whether \hat u is surjective, or whether \hat P is isomorphic to \hat Γ.

Mathematics Subject Classification: 20E18, 20F10, (57M07, 20F65)

Keywords and phrases:

Full text arXiv 1401.2790: pdf, ps.


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