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dc.contributor.authorCameron, Peter J.
dc.contributor.authorGadouleau, Maximilien
dc.contributor.authorMitchell, James D.
dc.contributor.authorPeresse, Yann
dc.date.accessioned2019-08-29T01:52:52Z
dc.date.available2019-08-29T01:52:52Z
dc.date.issued2017-06
dc.identifier.citationCameron , P J , Gadouleau , M , Mitchell , J D & Peresse , Y 2017 , ' Chains of subsemigroups ' , Israel Journal of Mathematics , vol. 220 , no. 1 , pp. 479–508 . https://doi.org/10.1007/s11856-017-1523-x
dc.identifier.issn0012-2172
dc.identifier.otherPURE: 10301041
dc.identifier.otherPURE UUID: be6c94a2-cf1c-4539-807d-bb5be5a50dde
dc.identifier.otherArXiv: http://arxiv.org/abs/1501.06394v1
dc.identifier.otherScopus: 85019021144
dc.identifier.urihttp://hdl.handle.net/2299/21631
dc.description.abstractWe investigate the maximum length of a chain of subsemigroups in various classes of semigroups, such as the full transformation semigroups, the general linear semigroups, and the semigroups of order-preserving transformations of finite chains. In some cases, we give lower bounds for the total number of subsemigroups of these semigroups. We give general results for finite completely regular and finite inverse semigroups. Wherever possible, we state our results in the greatest generality; in particular, we include infinite semigroups where the result is true for these. The length of a subgroup chain in a group is bounded by the logarithm of the group order. This fails for semigroups, but it is perhaps surprising that there is a lower bound for the length of a subsemigroup chain in the full transformation semigroup which is a constant multiple of the semigroup order.en
dc.format.extent10
dc.language.isoeng
dc.relation.ispartofIsrael Journal of Mathematics
dc.rightsEmbargoed
dc.subjectSEMIGROUPS
dc.subjectCombinatorics
dc.titleChains of subsemigroupsen
dc.contributor.institutionSchool of Physics, Astronomy and Mathematics
dc.contributor.institutionScience & Technology Research Institute
dc.contributor.institutionMathematics Research Group
dc.contributor.institutionUniversity of Hertfordshire
dc.description.statusPeer reviewed
dc.date.embargoedUntil2017-11-01
dc.identifier.urlhttps://arxiv.org/pdf/1501.06394v1.pdf
dc.relation.schoolSchool of Physics, Astronomy and Mathematics
dc.description.versiontypeFinal Accepted Version
dcterms.dateAccepted2017-06
rioxxterms.versionSMUR
rioxxterms.versionAM
rioxxterms.versionofrecordhttps://doi.org/10.1007/s11856-017-1523-x
rioxxterms.licenseref.startdate2017-11-01
rioxxterms.typeJournal Article/Review
herts.preservation.rarelyaccessedtrue
herts.date.embargo2017-11-01
herts.rights.accesstypeEmbargoed


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