  Let $K$ be a number field, and let $G\subset K^\times$ be a finitely
generated subgroup. Fix some prime number $\ell$, and consider the set of
primes $\mathfrak{p}$ of $K$ satisfying the following property: the reduction
of $G$ modulo $\mathfrak{p}$ is well-defined and has size coprime to $\ell$. We
give a closed--form expression for the density of this set.
