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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.
Original language | English |
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Pages (from-to) | 437-462 |
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
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Automata Languages Decidability: Automata, Languages, Decidability in Algebra
Ruskuc, N. (PI) & Quick, M. (CoI)
1/03/10 → 31/05/14
Project: Standard
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Finiteness Conditions and Index: Finiteness Conditions and Index in Semigroups and Monoids
Gray, R. D. (PI)
1/02/08 → 31/01/11
Project: Standard