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Automorphism groups of linearly ordered structures and endomorphisms of the ordered set ( Q ,≤) of rational numbers
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dc.contributor.author | McPhee, Jillian Dawn | |
dc.contributor.author | Mitchell, James David | |
dc.contributor.author | Quick, Martyn | |
dc.date.accessioned | 2018-08-31T13:30:05Z | |
dc.date.available | 2018-08-31T13:30:05Z | |
dc.date.issued | 2019-03 | |
dc.identifier | 244288055 | |
dc.identifier | e41e44cb-034c-4d24-856e-2eab9e527758 | |
dc.identifier | 85063791123 | |
dc.identifier | 000462721000008 | |
dc.identifier.citation | McPhee , 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/hay043 | en |
dc.identifier.issn | 0033-5606 | |
dc.identifier.other | ORCID: /0000-0002-5227-2994/work/58054917 | |
dc.identifier.other | ORCID: /0000-0002-5489-1617/work/73700805 | |
dc.identifier.uri | https://hdl.handle.net/10023/15924 | |
dc.description.abstract | We 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.extent | 24 | |
dc.format.extent | 416380 | |
dc.format.extent | 386999 | |
dc.language.iso | eng | |
dc.relation.ispartof | Quarterly Journal of Mathematics | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject | BDC | en |
dc.subject.lcc | QA | en |
dc.title | Automorphism groups of linearly ordered structures and endomorphisms of the ordered set ( Q ,≤) of rational numbers | en |
dc.type | Journal article | en |
dc.contributor.sponsor | EPSRC | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | 10.1093/qmath/hay043 | |
dc.description.status | Peer reviewed | en |
dc.date.embargoedUntil | 2019-08-28 | |
dc.identifier.grantnumber | EP/H011978/1 | en |
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