Definition of nilpotent in English:



  • Becoming zero when raised to some positive integral power.

    • ‘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.’


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