Theorems · Theorem · group theory
IsPGroup.isNilpotent
∀ {G : Type u_1} [hG : Group G] [Finite G] {p : ℕ} [hp : Fact (Nat.Prime p)], IsPGroup p G → Group.IsNilpotent GA p-group is nilpotent
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Finitestatement and proof · cited by 3,029
- Factstatement and proof · cited by 2,726
- Nontrivialproof · cited by 2,416
- HasQuotient.Quotientproof · cited by 2,301
- Nat.Primestatement and proof · cited by 2,059
- Nat.cardproof · cited by 844
- ne_of_gtproof · cited by 637
- Subgroup.centerproof · cited by 121
- IsPGroupstatement and proof · cited by 96
- Group.IsNilpotentstatement and proof · cited by 80
- Nat.card_posproof · cited by 36
Cited by1
Results whose statement or proof uses this declaration.
- Group.isNilpotent_of_product_of_sylow_groupproof · cited by 2