On Derek J.S. Robinson's A Course in the Theory of Groups, Hall's Criterion is:
If $N$ is a normal subgroup of $G$, and $N$ and G/N' are nilpotent, then $G$ is nilpotent.
There is an exercise:
Find an upper bound for the nilpotent class in Hall's criterion.
At first, I thought I was asked to find the upper bound for the nilpotent class of $G$ which satisfied the conditions ($N \lhd G$, $N$ and G/N' being nilpotent). But this wouldn't be possible, because for any nilpotent group $G$, if we take $N$ to be $G$ itself, then the conditions are certainly satisfied. I think this might means giving an upper bound for the nilpotent class of $G$ as a function of $c$ and $d$ if the nilpotent classes of $N$ and G/N' are $c$ and $d$ respectively.
Would you please give me some help, hints or references?
Many thanks.