Automorphism groups of finite topological rank

Itay Kaplan, Pierre Simon

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageAmerican English
Pages (from-to)2011-2043
Number of pages33
JournalTransactions of the American Mathematical Society
Issue number3
StatePublished - 1 Aug 2019

Bibliographical note

Publisher Copyright:
© 2019 Itay Kaplan and Pierre Simon.


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