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

Dolinka, Igor, Gray, Robert, McPhee, Jillian, Mitchell, James and Quick, Martyn (2016) Automorphism groups of countable algebraically closed graphs and endomorphisms of the random graph. Mathematical Proceedings of the Cambridge Philosophical Society, 160 (03). pp. 437-462. ISSN 0305-0041

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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.

Item Type:	Article
Uncontrolled Keywords:	existentially closed graphs, algebraically closed graphs,random graph,endomorphism monoid,countable universal graph, countable universal bipartite graph
Faculty \ School:	Faculty of Science > School of Mathematics
UEA Research Groups:	Faculty of Science > Research Groups > Algebra and Combinatorics
Related URLs:	http://arxiv.org/pdf/1408.4107.pdf
Depositing User:	Pure Connector
Date Deposited:	22 Mar 2016 09:12
Last Modified:	18 May 2023 00:26
URI:	https://ueaeprints.uea.ac.uk/id/eprint/57661
DOI:	10.1017/S030500411500078X

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