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, $$G$$ is metanilpotent if there is a normal subgroup $$N$$ such that both $$N$$ and $$G/N$$ are nilpotent.

The following are clear:


 * Every metanilpotent group is a solvable group.
 * Every subgroup and every quotient of a metanilpotent group is metanilpotent.