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.

References

• J.C. Lennox, D.J.S. Robinson, The Theory of Infinite Soluble Groups, Oxford University Press, 2004, ISBN 0198507283. P.27.
• D.J.S. Robinson, A Course in the Theory of Groups, GTM 80, Springer Verlag, 1996, ISBN 0387944613. P.150.