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Preprint Number 1295

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1295. Itay Kaplan and Pierre Simon
Automorphism groups of finite topological rank

Submission date: 6 September 2017


We offer a criterion for showing that the automorphism group of an ultrahomogeneous structure is topologically 2-generated and even has a cyclically dense conjugacy class. We then show how finite topological rank of the automorphism group of an ω-categorical structure can go down to reducts. Together, those results prove that a large number of ω-categorical structures that appear in the literature have an automorphism group of finite topological rank. In fact, we are not aware of any ω-categorical structure to which they do not apply (assuming the automorphism group has no compact quotients). We end with a few questions and conjectures.

Mathematics Subject Classification: 20B27, 03C15

Keywords and phrases:

Full text arXiv 1709.01918: pdf, ps.

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