Theorems · Theorem · group theory
of_quotient_center_nilpotent
Deprecated since 2026-03-25Use Group.of_quotient_center_nilpotent instead.
∀ {G : Type u_1} [inst : Group G], Group.IsNilpotent (G ⧸ Subgroup.center G) → Group.IsNilpotent GAlias of Group.of_quotient_center_nilpotent.
If the quotient by center G is nilpotent, then so is G.
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement · cited by 6,238
- Subgroupstatement · cited by 3,593
- HasQuotient.Quotientstatement · cited by 2,301
- Subgroup.centerstatement · cited by 121
- Group.IsNilpotentstatement · cited by 80
- Group.of_quotient_center_nilpotentproof · cited by 3
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