Automorphism groups of countable algebraically closed graphs and endomorphisms of the random graph
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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.
Dolinka , 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. 03 , pp. 437-462 . DOI: 10.1017/S030500411500078X
Mathematical Proceedings of the Cambridge Philosophical Society
© 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 journals.cambridge.org / https://dx.doi.org/10.1017/S030500411500078X
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