Nilpotent implies every normal subgroup is potentially characteristic

Statement
In a nilpotent group, every normal subgroup is a potentially characteristic subgroup: it can be realized as a characteristic subgroup inside a possibly bigger group.

Related facts

 * Finite normal implies potentially characteristic
 * Central implies potentially characteristic
 * Finite implies every normal subgroup is potentially characteristic
 * Abelian implies every subgroup is potentially characteristic

Facts used

 * 1) uses::Normal subgroup contained in hypercenter is potentially characteristic

Proof
The proof follows from fact (1), and the observation that the hypercenter of a nilpotent group equals the whole group.