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dc.contributor.authorEast, J.
dc.contributor.authorMitchell, James David
dc.contributor.authorPéresse, Y.
dc.identifier.citationEast , J , Mitchell , J D & Péresse , Y 2015 , ' Maximal subsemigroups of the semigroup of all mappings on an infinite set ' , Transactions of the American Mathematical Society , vol. 367 , no. 3 , pp. 1911-1944 .
dc.identifier.otherPURE: 23107193
dc.identifier.otherPURE UUID: d622aa4b-0740-4abc-883a-339349d48c2d
dc.identifier.otherScopus: 84916620178
dc.identifier.otherORCID: /0000-0002-5489-1617/work/73700777
dc.identifier.otherWOS: 000351857000014
dc.description.abstractIn this paper we classify the maximal subsemigroups of the full transformation semigroup ΩΩ, which consists of all mappings on the infinite set Ω, containing certain subgroups of the symmetric group Sym (Ω) on Ω. In 1965 Gavrilov showed that there are five maximal subsemigroups of ΩΩ containing Sym (Ω) when Ω is countable, and in 2005 Pinsker extended Gavrilov's result to sets of arbitrary cardinality. We classify the maximal subsemigroups of ΩΩ on a set Ω of arbitrary infinite cardinality containing one of the following subgroups of Sym (Ω): the pointwise stabiliser of a non-empty finite subset of Ω, the stabiliser of an ultrafilter on Ω, or the stabiliser of a partition of Ω into finitely many subsets of equal cardinality. If G is any of these subgroups, then we deduce a characterisation of the mappings f, g ∈ ΩΩ such that the semigroup generated by G ∪ {f, g} equals ΩΩ.
dc.relation.ispartofTransactions of the American Mathematical Societyen
dc.rights© 2014. American Mathematical Society. First published in Transactions of the American Mathematical Society 2014.en
dc.subjectQA Mathematicsen
dc.titleMaximal subsemigroups of the semigroup of all mappings on an infinite seten
dc.typeJournal articleen
dc.description.versionPublisher PDFen
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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