Theorems · Theorem · group theory
Group.of_quotient_center_nilpotent
∀ {G : Type u_1} [inst : Group G], Group.IsNilpotent (G ⧸ Subgroup.center G) → Group.IsNilpotent GIf the quotient by center G is nilpotent, then so is G.
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Subgroup.comapproof · cited by 154
- Subgroup.centerstatement and proof · cited by 121
- QuotientGroup.mk'proof · cited by 90
- Group.IsNilpotentstatement and proof · cited by 80
- Subgroup.upperCentralSeriesproof · cited by 51
- Subgroup.comap_topproof · cited by 10
- Group.IsNilpotent.nilpotentproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Group.nilpotencyClass_quotient_centerproof · cited by 3
- IsPGroup.isNilpotentproof · cited by 1
- of_quotient_center_nilpotentproof · cited by 0