Homogeneity in the free group
Group Theory
2019-12-19 v1 Logic
Abstract
We show that any non abelian free group is strongly -homogeneous, i.e. that finite tuples of elements which satisfy the same first-order properties are in the same orbit under . 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 -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