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https://open.uns.ac.rs/handle/123456789/31347
Title: | Automorphism groups of countable algebraically closed graphs and endomorphisms of the random graph | Authors: | Dolinka Igor Gray Robert D. McPhee Jillian D. Mitchell James D. Quick Martyn |
Issue Date: | 2016 | Journal: | Mathematical Proceedings of the Cambridge Philosophical Society | Abstract: | Copyright © Cambridge Philosophical Society 2016. 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. | URI: | https://open.uns.ac.rs/handle/123456789/31347 | ISSN: | 0305-0041 | DOI: | 10.1017/S030500411500078X |
Appears in Collections: | PMF Publikacije/Publications |
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