English

Groups with infinitely many ends are not fraction groups

Group Theory 2015-06-08 v2

Abstract

We show that any finitely generated group FF with infinitely many ends is not a group of fractions of any finitely generated proper subsemigroup PP, that is FF cannot be expressed as a product PP1P P^{-1}. In particular this solves a conjecture of Navas in the positive. As a corollary we obtain a new proof of the fact that finitely generated free groups do not admit isolated left-invariant orderings.

Keywords

Cite

@article{arxiv.1303.1656,
  title  = {Groups with infinitely many ends are not fraction groups},
  author = {Dawid Kielak},
  journal= {arXiv preprint arXiv:1303.1656},
  year   = {2015}
}

Comments

Rewritten to accommodate referees comments. Identical to the published version

R2 v1 2026-06-21T23:38:08.108Z