  Let $G$ be a finite nilpotent group and $K$ a number field with torsion
relatively prime to the order of $G$. By a sequence of central group extensions
with cyclic kernel we obtain an upper bound for the minimum number of prime
ideals of $K$ ramified in a Galois extension of $K$ with Galois group
isomorphic to $G$. This sharpens and extends results of Geyer and Jarden and of
Plans. Also we confirm Boston's conjecture on the minimum number of ramified
primes for a family of central extensions by the Schur multiplicator.
