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arXiv · 1408.4107

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

Igor Dolinka·Robert D. Gray·Jillian D. McPhee·James D. 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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Igor Dolinka, Robert D. Gray, Jillian D. McPhee, James D. Mitchell, Martyn Quick. 2015-11-11. Automorphism groups of countable algebraically closed graphs and endomorphisms of the random graph. https://doi.org/10.1017/s030500411500078x

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