Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 676

Preprint Number 676

Previous Next Preprint server

676. Martin R. Bridson and Henry Wilton
The isomorphism problem for profinite completions of residually finite groups

Submission date: 13 January 2014


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.

Last updated: January 19 2014 16:41 Please send your corrections to: