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In mathematics, in the field of group theo … 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.of a metanilpotent group is metanilpotent.
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| rdfs:comment |
In mathematics, in the field of group theo … 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.of a metanilpotent group is metanilpotent.
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Metanilpotent group
|
