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, is metanilpotent if there is a normal subgroup such that both and are nilpotent.
The following are clear:
- Every metanilpotent group is a solvable group.
- Every subgroup and every quotient of a metanilpotent group is metanilpotent.