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dc.contributor.authorDolinka, Igor
dc.contributor.authorGray, Robert Duncan
dc.contributor.authorMcPhee, Jillian Dawn
dc.contributor.authorMitchell, James David
dc.contributor.authorQuick, Martyn
dc.identifier.citationDolinka , I , Gray , R D , McPhee , J D , Mitchell , J D & Quick , M 2016 , ' Automorphism groups of countable algebraically closed graphs and endomorphisms of the random graph ' , Mathematical Proceedings of the Cambridge Philosophical Society , vol. 160 , no. 3 , pp. 437-462 .
dc.identifier.otherPURE: 21569010
dc.identifier.otherPURE UUID: 016f9aa6-521d-486e-923b-577c66302168
dc.identifier.otherScopus: 84955253873
dc.identifier.otherORCID: /0000-0002-5227-2994/work/58054918
dc.identifier.otherWOS: 000379503000005
dc.identifier.otherORCID: /0000-0002-5489-1617/work/73700809
dc.description.abstractWe establish links between countable algebraically closed graphs and the endomorphisms of the countable universal graph R. As a consequence we show that, for any countable graph Γ, there are uncountably many maximal subgroups of the endomorphism monoid of R isomorphic to the automorphism group of Γ. Further structural information about End R is established including that Aut Γ arises in uncountably many ways as a Schützenberger group. Similar results are proved for the countable universal directed graph and the countable universal bipartite graph.
dc.relation.ispartofMathematical Proceedings of the Cambridge Philosophical Societyen
dc.rights© 2016, Publisher / the Author(s). 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.subjectExistentially closed graphsen
dc.subjectAlgebraically closed graphsen
dc.subjectRandom graphen
dc.subjectEndomorphism monoiden
dc.subjectCountable universal graphen
dc.subjectCountable universal bipartite graphen
dc.subjectQA Mathematicsen
dc.titleAutomorphism groups of countable algebraically closed graphs and endomorphisms of the random graphen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews.Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews.School of Mathematics and Statisticsen
dc.contributor.institutionUniversity of St Andrews.Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden

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