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Undecidability and the developability of permutoids and rigid pseudogroups

dc.creatorBridson, MR
dc.creatorWilton, Henry John
dc.date.accessioned2017-01-10
dc.date.accessioned2018-11-24T23:27:05Z
dc.date.available2017-03-27T08:22:05Z
dc.date.available2018-11-24T23:27:05Z
dc.date.issued2017-03-20
dc.identifierhttps://www.repository.cam.ac.uk/handle/1810/263240
dc.identifier.urihttp://repository.aust.edu.ng/xmlui/handle/123456789/3942
dc.description.abstractA $\textit{permutoid}$ is a set of partial permutations that contains the identity and is such that partial compositions, when defined, have at most one extension in the set. In 2004 Peter Cameron conjectured that there can exist no algorithm that determines whether or not a permutoid based on a finite set can be completed to a finite permutation group. In this note we prove Cameron’s conjecture by relating it to our recent work on the profinite triviality problem for finitely presented groups. We also prove that the existence problem for finite developments of rigid pseudogroups is unsolvable. In an appendix, Steinberg recasts these results in terms of inverse semigroups.
dc.languageen
dc.publisherCambridge University Press
dc.publisherForum of Mathematics, Sigma
dc.rightshttp://creativecommons.org/licenses/by/4.0/
dc.rightshttp://creativecommons.org/licenses/by/4.0/
dc.rightshttp://creativecommons.org/licenses/by/4.0/
dc.rightsAttribution 4.0 International
dc.rightsAttribution 4.0 International
dc.rightsAttribution 4.0 International
dc.titleUndecidability and the developability of permutoids and rigid pseudogroups
dc.typeArticle


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