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

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Date
05/2016
Author
Dolinka, Igor
Gray, Robert Duncan
McPhee, Jillian Dawn
Mitchell, James David
Quick, Martyn
Keywords
Existentially closed graphs
Algebraically closed graphs
Random graph
Endomorphism monoid
Countable universal graph
Countable universal bipartite graph
QA Mathematics
T-NDAS
BDC
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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.
Citation
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. 3 , pp. 437-462 . https://doi.org/10.1017/S030500411500078X
Publication
Mathematical Proceedings of the Cambridge Philosophical Society
Status
Peer reviewed
DOI
https://doi.org/10.1017/S030500411500078X
ISSN
0305-0041
Type
Journal article
Rights
© 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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  • University of St Andrews Research
URL
http://arxiv.org/abs/1408.4107
URI
http://hdl.handle.net/10023/9178

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