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Universal sequences for the order-automorphisms of the rationals
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dc.contributor.author | Hyde, J. | |
dc.contributor.author | Jonusas, J. | |
dc.contributor.author | Mitchell, J. D. | |
dc.contributor.author | Peresse, Y. H. | |
dc.date.accessioned | 2016-06-21T12:30:06Z | |
dc.date.available | 2016-06-21T12:30:06Z | |
dc.date.issued | 2016-08 | |
dc.identifier | 241562474 | |
dc.identifier | 2c360f24-5c60-4c04-9dc4-cff3cf77e430 | |
dc.identifier | 85045835715 | |
dc.identifier | 000380942800002 | |
dc.identifier.citation | Hyde , 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/jdw015 | en |
dc.identifier.issn | 0024-6107 | |
dc.identifier.other | ArXiv: http://arxiv.org/abs/1401.7823v3 | |
dc.identifier.other | ORCID: /0000-0002-5489-1617/work/73700787 | |
dc.identifier.uri | https://hdl.handle.net/10023/9024 | |
dc.description.abstract | In 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.extent | 17 | |
dc.format.extent | 300463 | |
dc.language.iso | eng | |
dc.relation.ispartof | Journal of the London Mathematical Society | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject | BDC | en |
dc.subject | R2C | en |
dc.subject.lcc | QA | en |
dc.title | Universal sequences for the order-automorphisms of the rationals | en |
dc.type | Journal article | 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 | 10.1112/jlms/jdw015 | |
dc.description.status | Peer reviewed | en |
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