Definition of nilpotent in English:



  • Becoming zero when raised to some positive integral power.

    • ‘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 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.’
    • ‘After completely reducible systems, the notions of solvable and nilpotent systems are discussed, where general identities are considered instead of the usual commutativity.’
    • ‘He used the, now familiar, tools of idempotent and nilpotent elements.’
    • ‘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.’


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