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Approximation of automorphisms of the rationals and the random graph

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Abstract

Let G be the group of order-preserving automorphisms of the rationals Q, or the
group of colour-preserving automorphisms of the C-coloured random graph RC. We show that given any non-identity f A G, there exists g A G such that every automorphism in G is the limit of a sequence of automorphisms generated by f and g. Moreover, if, in some sense, f has no finite structure, then g can be chosen with a great deal of flexibility.
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Original languageEnglish
Pages (from-to)361-388
Number of pages28
JournalJournal of Group Theory
Volume14
Issue number3
Early online date31 Aug 2010
DOIs
Publication statusPublished - 2011

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