Projects per year
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.
Original language  English 

Pages (fromto)  437462 
Number of pages  26 
Journal  Mathematical Proceedings of the Cambridge Philosophical Society 
Volume  160 
Issue number  3 
Early online date  21 Jan 2016 
DOIs  
Publication status  Published  May 2016 
Keywords
 Existentially closed graphs
 Algebraically closed graphs
 Random graph
 Endomorphism monoid
 Countable universal graph
 Countable universal bipartite graph
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Dive into the research topics of 'Automorphism groups of countable algebraically closed graphs and endomorphisms of the random graph'. Together they form a unique fingerprint.Projects
 2 Finished

Automata Languages Decidability: Automata, Languages, Decidability in Algebra
1/03/10 → 31/05/14
Project: Standard

Finiteness Conditions and Index: Finiteness Conditions and Index in Semigroups and Monoids
Gray, R. D.
1/02/08 → 31/01/11
Project: Standard
Profiles

Martyn Quick
Person: Academic