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**roninpro** Hello. I have been asked to prove the following:

If $\displaystyle N$ is a normal subgroup of a nilpotent group $\displaystyle G$, then $\displaystyle N \cap Z(G)$ is nontrivial.

I attempted to take the factor group $\displaystyle G/N$ (since it too is solvable) and try to deal with the image of $\displaystyle Z(G)$ under the canonical homomorphism, but I can't get the result to come out.

This is extremely frustrating, and thus, I would appreciate any suggestions you may have. (Though, I am not necessarily searching for a complete solution.)

Thank you.