Definition of nilpotent in English:

nilpotent

adjective nɪlˈpəʊt(ə)ntnilˈpōtnt

Mathematics

Becoming zero when raised to some positive integral power.
〔数〕幂零的
Example sentencesExamples
- After completely reducible systems, the notions of solvable and nilpotent systems are discussed, where general identities are considered instead of the usual commutativity.
- He introduced the idea of a normal form which he used in the solution of the word problem for Lie rings and also for nilpotent groups.
- He showed that the Frattini subgroup is nilpotent and, in so doing, used the beautiful method of proof known today as the ‘Frattini argument‘.
- All Hirsch's publications were in group theory, in addition to the work on polycyclic groups he published on locally nilpotent groups and automorphism groups of torsion free abelian groups.
- He used the, now familiar, tools of idempotent and nilpotent elements.

Origin

Late 19th century: from nil + Latin potens, potent- 'power'.

Definition of nilpotent in US English:

nilpotent

adjectivenilˈpōtnt

Mathematics

Equal to zero when raised to a positive integral power.
〔数〕幂零的
Example sentencesExamples
- After completely reducible systems, the notions of solvable and nilpotent systems are discussed, where general identities are considered instead of the usual commutativity.
- All Hirsch's publications were in group theory, in addition to the work on polycyclic groups he published on locally nilpotent groups and automorphism groups of torsion free abelian groups.
- He showed that the Frattini subgroup is nilpotent and, in so doing, used the beautiful method of proof known today as the ‘Frattini argument‘.
- He used the, now familiar, tools of idempotent and nilpotent elements.
- He introduced the idea of a normal form which he used in the solution of the word problem for Lie rings and also for nilpotent groups.

Origin

Late 19th century: from nil + Latin potens, potent- ‘power’.

单词	nilpotent
释义	Definition of nilpotent in English: nilpotent adjective nɪlˈpəʊt(ə)ntnilˈpōtnt Mathematics Becoming zero when raised to some positive integral power. 〔数〕幂零的 Example sentencesExamples After completely reducible systems, the notions of solvable and nilpotent systems are discussed, where general identities are considered instead of the usual commutativity. He introduced the idea of a normal form which he used in the solution of the word problem for Lie rings and also for nilpotent groups. He showed that the Frattini subgroup is nilpotent and, in so doing, used the beautiful method of proof known today as the ‘Frattini argument‘. All Hirsch's publications were in group theory, in addition to the work on polycyclic groups he published on locally nilpotent groups and automorphism groups of torsion free abelian groups. He used the, now familiar, tools of idempotent and nilpotent elements. Origin Late 19th century: from nil + Latin potens, potent- 'power'. Definition of nilpotent in US English: nilpotent adjectivenilˈpōtnt Mathematics Equal to zero when raised to a positive integral power. 〔数〕幂零的 Example sentencesExamples After completely reducible systems, the notions of solvable and nilpotent systems are discussed, where general identities are considered instead of the usual commutativity. All Hirsch's publications were in group theory, in addition to the work on polycyclic groups he published on locally nilpotent groups and automorphism groups of torsion free abelian groups. He showed that the Frattini subgroup is nilpotent and, in so doing, used the beautiful method of proof known today as the ‘Frattini argument‘. He used the, now familiar, tools of idempotent and nilpotent elements. He introduced the idea of a normal form which he used in the solution of the word problem for Lie rings and also for nilpotent groups. Origin Late 19th century: from nil + Latin potens, potent- ‘power’.
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