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Overgroups of the automorphism group of the Rado graph. (English) Zbl 1266.05052
Ludwig, Monika (ed.) et al., Asymptotic geometric analysis. Proceedings of the fall 2010 Fields Institute thematic program. New York, NY: Springer; Toronto: The Fields Institute for Research in the Mathematical Sciences (ISBN 978-1-4614-6405-1/hbk; 978-1-4614-6406-8/ebook). Fields Institute Communications 68, 45-54 (2013).
Summary: We are interested in overgroups of the automorphism group of the Rado graph. One class of such overgroups is completely understood; this is the class of reducts. In this article we tie recent work on various other natural overgroups, in particular establishing group connections between them and the reducts.
For the entire collection see [Zbl 1262.00011].

MSC:
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
05C80 Random graphs (graph-theoretic aspects)
05C60 Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)
05C65 Hypergraphs
05C63 Infinite graphs
20F28 Automorphism groups of groups
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