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1Mathematics Institute, North Haugh, St Andrews, Fife, KY16 9SS, United Kingdom
2Mathematics Department, University of Louisville, Louisville, KY40292, U.S.A.
Citation Information: Journal of Group Theory. Volume 14, Issue 3, Pages 361–388, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: 10.1515/jgt.2010.057, October 2010
Let G be the group of order-preserving automorphisms of the rationals ℚ, or the group of colour-preserving automorphisms of the -coloured random graph
. We show that given any non-identity ƒ ∈ G, there exists g ∈ G such that every automorphism in G is the limit of a sequence of automorphisms generated by ƒ and g. Moreover, if, in some sense, ƒ has no finite structure, then g can be chosen with a great deal of flexibility.
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