Finitely generated and nilpotent implies Hopfian

Statement
Any finitely generated nilpotent group is a Hopfian group.

Facts used

 * 1) uses::Equivalence of definitions of finitely generated nilpotent group: In particular, the equivalence of interest is that for a nilpotent group, being finitely generated is equivalent to being Noetherian (i.e., every subgroup is finitely generated).
 * 2) uses::Noetherian implies Hopfian

Proof
The proof follows directly by combining Facts (1) and (2).