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dc.contributor.authorMcPhee, Jillian Dawn
dc.contributor.authorMitchell, James David
dc.contributor.authorQuick, Martyn
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 .
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.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.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
dc.subjectQA Mathematicsen
dc.titleAutomorphism groups of linearly ordered structures and endomorphisms of the ordered set ( Q ,≤) of rational numbersen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden

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