Coset-minimal groups

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dc.authoridVerbovskiy, Viktor/0000-0001-5177-8523
dc.authorwosidVerbovskiy, Viktor/D-6255-2013
dc.contributor.authorBelegradek, O
dc.contributor.authorVerbovskiy, V
dc.contributor.authorWagner, FO
dc.date.accessioned2024-07-18T20:56:54Z
dc.date.available2024-07-18T20:56:54Z
dc.date.issued2003
dc.departmentİstanbul Bilgi Üniversitesien_US
dc.description.abstractA totally ordered group G (possibly with extra structure) is called coset-minimal if every definable subset of G is a finite union of cosets of definable subgroups intersected with intervals with endpoints in G boolean OR {+/-infinity}. Continuing work in Belegradek et al. (J. Symbolic Logic 65(3) (2000) 1115) and Point and Wagner (Ann. Pure Appl. Logic 105(1-3) (2000) 261), we study coset-minimality, as well as two weak versions of the notion: eventual and ultimate coset-minimality. These groups are abelian, an eventually coset-minimal group, as a pure ordered group, is an ordered abelian group of finite regular rank. Any pure ordered abelian group of finite regular rank is ultimately coset-minimal and has the exchange property; moreover, every definable function in such a group is piecewise linear. Pure coset-minimal and eventually coset-minimal groups are classified. In a discrete coset-minimal group every definable unary function is piece-wise linear (this improves a result in Point and Wagner (Ann. Pure Appl. Logic 105(1-3) (2000) 261), where coset-minimality of the theory of the group was required). A dense coset-minimal group has the exchange property (which is false in the discrete case (M.S.R.I., preprint series, 1998-051)); moreover, any definable unary function is piecewise linear, except possibly for finitely many cosets of the smallest definable convex nonzero subgroup. Finally, we give some examples and open questions. (C) 2002 Elsevier Science B.V. All rights reserved.en_US
dc.identifier.doi10.1016/S0168-0072(02)00084-2
dc.identifier.endpage143en_US
dc.identifier.issn0168-0072
dc.identifier.issue2.Maren_US
dc.identifier.scopus2-s2.0-0038354026en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.startpage113en_US
dc.identifier.urihttps://doi.org/10.1016/S0168-0072(02)00084-2
dc.identifier.urihttps://hdl.handle.net/11411/8876
dc.identifier.volume121en_US
dc.identifier.wosWOS:000183901000001en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherElsevier Science Bven_US
dc.relation.ispartofAnnals of Pure and Applied Logicen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectCoset-Minimalityen_US
dc.subjectPiecewise Linearen_US
dc.subjectExchange Propertyen_US
dc.subjectRegular Ranken_US
dc.subjectOrdered Structuresen_US
dc.subjectDefinable Setsen_US
dc.titleCoset-minimal groupsen_US
dc.typeArticleen_US

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