English

Homogeneity in the free group

Group Theory 2019-12-19 v1 Logic

Abstract

We show that any non abelian free group \F\F is strongly 0\aleph_0-homogeneous, i.e. that finite tuples of elements which satisfy the same first-order properties are in the same orbit under \Aut(\F)\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 0\aleph_0-homogeneous.

Keywords

Cite

@article{arxiv.1003.4095,
  title  = {Homogeneity in the free group},
  author = {Chloé Perin and Rizos Sklinos},
  journal= {arXiv preprint arXiv:1003.4095},
  year   = {2019}
}

Comments

26 pages

R2 v1 2026-06-21T15:00:36.105Z