Groups with infinitely many ends are not fraction groups. (Q2347654)

Summary: We show that any finitely generated group \(F\) with infinitely many ends is not a group of fractions of any finitely generated proper subsemigroup \(P\), that is \(F\) cannot be expressed as a product \(PP^{-1}\). 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.