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dc.contributor.authorMcPhee, Jillian Dawn
dc.contributor.authorMitchell, James David
dc.contributor.authorQuick, Martyn
dc.date.accessioned2018-08-31T13:30:05Z
dc.date.available2018-08-31T13:30:05Z
dc.date.issued2019-03
dc.identifier.citationMcPhee , J D , Mitchell , J D & Quick , M 2019 , ' Automorphism groups of linearly ordered structures and endomorphisms of the ordered set ( Q ,≤) of rational numbers ' , Quarterly Journal of Mathematics , vol. 70 , no. 1 , pp. 171-194 . https://doi.org/10.1093/qmath/hay043en
dc.identifier.issn0033-5606
dc.identifier.otherPURE: 244288055
dc.identifier.otherPURE UUID: e41e44cb-034c-4d24-856e-2eab9e527758
dc.identifier.otherORCID: /0000-0002-5227-2994/work/58054917
dc.identifier.otherScopus: 85063791123
dc.identifier.otherWOS: 000462721000008
dc.identifier.otherORCID: /0000-0002-5489-1617/work/73700805
dc.identifier.urihttps://hdl.handle.net/10023/15924
dc.description.abstractWe investigate the structure of the monoid of endomorphisms of the ordered set ( Q ,≤) of rational numbers. We show that for any countable linearly ordered set Ω, there are uncountably many maximal subgroups of End( Q ,≤) isomorphic to the automorphism group of Ω. We characterize those subsets X of Q that arise as a retract in ( Q ,≤) in terms of topological information concerning X. Finally, we establish that a countable group arises as the automorphism group of a countable linearly ordered set, and hence as a maximal subgroup of End( Q ,≤), if and only if it is free abelian of finite rank.
dc.format.extent24
dc.language.isoeng
dc.relation.ispartofQuarterly Journal of Mathematicsen
dc.rights© 2018, the Author(s). Published by Oxford University Press. This work has been made available online in accordance with the publisher’s policies. This is the author created accepted version manuscript following peer review and as such may differ slightly from the final published version. The final published version of this work is available at https://doi.org/https://doi.org/10.1093/qmath/hay043en
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subjectBDCen
dc.subject.lccQAen
dc.titleAutomorphism groups of linearly ordered structures and endomorphisms of the ordered set ( Q ,≤) of rational numbersen
dc.typeJournal articleen
dc.contributor.sponsorEPSRCen
dc.description.versionPreprinten
dc.description.versionPostprinten
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.identifier.doihttps://doi.org/10.1093/qmath/hay043
dc.description.statusPeer revieweden
dc.date.embargoedUntil2019-08-28
dc.identifier.grantnumberEP/H011978/1en


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