Abstract
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 language | English |
|---|---|
| Pages (from-to) | 2635-2668 |
| Number of pages | 34 |
| Journal | Duke Mathematical Journal |
| Volume | 161 |
| Issue number | 13 |
| DOIs | |
| State | Published - 2012 |
| Externally published | Yes |