Automorphism groups of finite topological rank

Itay Kaplan, Pierre Simon

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

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
Volume372
Issue number3
DOIs
StatePublished - 1 Aug 2019

Bibliographical note

Publisher Copyright:
© 2019 Itay Kaplan and Pierre Simon.

Fingerprint

Dive into the research topics of 'Automorphism groups of finite topological rank'. Together they form a unique fingerprint.

Cite this