Hello. I have been asked to prove the following:
If is a nontrivial normal subgroup of a nilpotent group , then is nontrivial.
I attempted to take the factor group (since it too is nilpotent) and try to deal with the image of 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.
Sorry for the mistakes - I typed up the post in a hurry.
I originally went about halfway in the direction of your solution but couldn't see what to do with it, so I discarded it, unfortunately.
I see how to do it now. Thank you very much for your response.