  Let N be a normal subgroup of a finite group G and consider the set cd(G|N)
of degrees of irreducible characters of G whose kernels do not contain N. A
number of theorems are proved relating the set cd(G|N) to the structure of N.
For example, if N is solvable, its derived length is bounded above by a
function of |cd(G|N)|. Also, if |cd(G|N)| is at most 2, then N is solvable and
its derived length is at most |cd(G|N)|. If G is solvable and |cd(G|N)| = 3,
then the derived length of N is at most 3.
