Metanilpotent group
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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 nilpotent 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 polynilpotent group.
- Every metanilpotent group is a solvable group.
- Every subgroup and every quotient of a metanilpotent group is metanilpotent.
