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dc.contributor.authorHyde, J.
dc.contributor.authorJonusas, J.
dc.contributor.authorMitchell, J. D.
dc.contributor.authorPeresse, Y. H.
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 .
dc.identifier.otherPURE: 241562474
dc.identifier.otherPURE UUID: 2c360f24-5c60-4c04-9dc4-cff3cf77e430
dc.identifier.otherScopus: 85045835715
dc.identifier.otherWOS: 000380942800002
dc.identifier.otherORCID: /0000-0002-5489-1617/work/73700787
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.relation.ispartofJournal of the London Mathematical Societyen
dc.rights© 2016, London Mathematical Society. This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at
dc.subjectQA Mathematicsen
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.description.statusPeer revieweden

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