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dc.contributor.authorHyde, J.
dc.contributor.authorJonusas, J.
dc.contributor.authorMitchell, J. D.
dc.contributor.authorPeresse, Y. H.
dc.date.accessioned2016-06-21T12:30:06Z
dc.date.available2016-06-21T12:30:06Z
dc.date.issued2016-08
dc.identifier241562474
dc.identifier2c360f24-5c60-4c04-9dc4-cff3cf77e430
dc.identifier85045835715
dc.identifier000380942800002
dc.identifier.citationHyde , J , Jonusas , J , Mitchell , J D & Peresse , Y H 2016 , ' Universal sequences for the order-automorphisms of the rationals ' , Journal of the London Mathematical Society , vol. 94 , no. 1 , pp. 21-37 . https://doi.org/10.1112/jlms/jdw015en
dc.identifier.issn0024-6107
dc.identifier.otherArXiv: http://arxiv.org/abs/1401.7823v3
dc.identifier.otherORCID: /0000-0002-5489-1617/work/73700787
dc.identifier.urihttps://hdl.handle.net/10023/9024
dc.description.abstractIn this paper, we consider the group Aut(Q,≤) of order-automorphisms of the rational numbers, proving a result analogous to a theorem of Galvin's for the symmetric group. In an announcement, Khélif states that every countable subset of Aut(Q,≤) is contained in an N-generated subgroup of Aut(Q,≤) for some fixed N ∈ N. We show that the least such N is 2. Moreover, for every countable subset of Aut(Q,≤), we show that every element can be given as a prescribed product of two generators without using their inverses. More precisely, suppose that a and b freely generate the free semigroup {a,b}+ consisting of the non-empty words over a and b. Then we show that there exists a sequence of words w1, w2,... over {a,b} such that for every sequence f1, f2, ... ∈ Aut(Q,≤) there is a homomorphism φ : {a,b}+ → Aut(Q,≤) where (wi)φ=fi for every i. As a corollary to the main theorem in this paper, we obtain a result of Droste and Holland showing that the strong cofinality of Aut(Q,≤) is uncountable, or equivalently that Aut(Q,≤) has uncountable cofinality and Bergman's property.
dc.format.extent17
dc.format.extent300463
dc.language.isoeng
dc.relation.ispartofJournal of the London Mathematical Societyen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subjectBDCen
dc.subjectR2Cen
dc.subject.lccQAen
dc.titleUniversal sequences for the order-automorphisms of the rationalsen
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.identifier.doi10.1112/jlms/jdw015
dc.description.statusPeer revieweden


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