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Automorphism groups of countable algebraically closed graphs and endomorphisms of the random graph

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Author(s)

Igor Dolinka, Robert Duncan Gray, Jillian Dawn McPhee, James David Mitchell, Martyn Quick

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Abstract

We 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.

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Original languageEnglish
Pages (from-to)437-462
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume160
Issue number03
Early online date21 Jan 2016
DOIs
Publication statusPublished - May 2016

    Research areas

  • Existentially closed graphs, Algebraically closed graphs, Random graph, Endomorphism monoid, Countable universal graph, Countable universal bipartite graph

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