Metanilpotent group

In mathematics, in the field of group theory, a metanilpotent group is a group that is nilpotent by nilpotent. In other words, it has a normal nilpotent subgroup such that the quotient group is also nilpotent.
In symbols, formula_1 is metanilpotent if there is a normal subgroup formula_2 such that both formula_2 and formula_4 are nilpotent.
The following are clear: