Groups with infinitely many ends are not fraction groups
Dawid KielakUniversität Bonn, Germany
We show that any finitely generated group with infinitely many ends is not a group of fractions of any finitely generated proper subsemigroup , that is cannot be expressed as a product . 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.
Cite this article
Dawid Kielak, Groups with infinitely many ends are not fraction groups. Groups Geom. Dyn. 9 (2015), no. 1, pp. 317–323DOI 10.4171/GGD/314