Theorems · Theorem · group theory
IsCyclic.normalizer_le_centralizer
∀ {G : Type u_3} [inst : Group G] [Finite G] {p : ℕ},
(Nat.card G).minFac = p → ∀ {P : Sylow p G}, IsCyclic ↥↑P → Subgroup.normalizer ↑P ≤ Subgroup.centralizer ↑P- Defined in
- Mathlib.GroupTheory.Transfer
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites54
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Finitestatement and proof · cited by 3,029
- Factproof · cited by 2,726
- HasQuotient.Quotientproof · cited by 2,301
- le_reflproof · cited by 2,061
- Nat.Primeproof · cited by 2,059
- LT.lt.ne'proof · cited by 1,417
- pow_zeroproof · cited by 1,094
- Nat.cardstatement and proof · cited by 844
- Fact.outproof · cited by 328
Cited by2
Results whose statement or proof uses this declaration.
- IsCyclic.isComplement'statement and proof · cited by 1
- IsZGroup.commutator_ltproof · cited by 0