Becoming zero when raised to some 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.
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