Theorems · Theorem · group theory
Subgroup.le_normalizer_iff_commutator_le_left
∀ {G : Type u_1} [inst : Group G] {H K : Subgroup G}, H ≤ Subgroup.normalizer ↑K ↔ ⁅K, H⁆ ≤ K- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Bracket.bracketstatement · cited by 642
- Subgroup.normalizerstatement · cited by 108
- Subgroup.commutator_commproof · cited by 7
- Subgroup.le_normalizer_iff_commutator_le_rightproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.lowerCentralSeries_antitoneproof · cited by 3