Homogeneity in the free group

Chloé Perin*, Rizos Sklinos

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


We show that any nonabelian free group F is strongly א0-homogeneous, that is, that finite tuples of elements which satisfy the same first-order properties are in the same orbit under Aut(F). We give a characterization of elements in finitely generated groups which have the same first-order properties as a primitive element of the free group. We deduce as a consequence that most hyperbolic surface groups are not strongly א0-homogeneous.

Original languageAmerican English
Pages (from-to)2635-2668
Number of pages34
JournalDuke Mathematical Journal
Issue number13
StatePublished - 2012
Externally publishedYes


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