  We answer a question raised by Hindry and Ratazzi concerning the intersection
between cyclotomic extensions of a number field $K$ and extensions of $K$
generated by torsion points of an abelian variety over $K$. We prove that a
weak version of the property $(\mu)$ they introduced holds for any abelian
variety, while the same is not true for a slightly stronger version of the
property they also considered.
