  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 $P P^{-1}$. 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.
