Equal to zero when raised to a positive integral power.
- He used the, now familiar, tools of idempotent and nilpotent elements.
- 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.
Late 19th century: from nil + Latin potens, potent- 'power'.
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