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The Triviality problem for profinite completions

dc.creatorBridson, Martin R
dc.creatorWilton, Henry John
dc.date.accessioned2018-11-24T23:26:22Z
dc.date.available2015-02-25T12:19:09Z
dc.date.available2018-11-24T23:26:22Z
dc.date.issued2015-02-24
dc.identifierhttps://www.repository.cam.ac.uk/handle/1810/246916
dc.identifier.urihttp://repository.aust.edu.ng/xmlui/handle/123456789/3814
dc.description.abstractWe prove that there is no algorithm that can determine whether or not a finitely presented group has a non-trivial finite quotient; indeed, this property remains undecidable among the fundamental groups of compact, non-positively curved square complexes. We deduce that many other properties of groups are undecidable. For hyperbolic groups, there cannot exist algorithms to determine largeness, the existence of a linear representation with infinite image (over any infinite field), or the rank of the profinite completion.
dc.languageen
dc.publisherSpringer
dc.publisherInventiones Mathematicae
dc.titleThe Triviality problem for profinite completions
dc.typeArticle


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