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About: Metanilpotent group     Goto   Sponge   NotDistinct   Permalink

An Entity of Type : yago:WikicatPropertiesOfGroups, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)

Type: yago:WikicatSolvableGroupsyago:Abstraction100002137yago:Group100031264yago:Possession100032613yago:Property113244109yago:Relation100031921yago:WikicatPropertiesOfGroups New Facet based on Instances of this Class

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.