Theorems · Theorem · group theory
Subgroup.commutator_le
∀ {G : Type u_1} [inst : Group G] {H₁ H₂ H₃ : Subgroup G}, ⁅H₁, H₂⁆ ≤ H₃ ↔ ∀ g₁ ∈ H₁, ∀ g₂ ∈ H₂, ⁅g₁, g₂⁆ ∈ H₃- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 70 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.coeproof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Set.ofPredproof · cited by 6,101
- Subgroupstatement and proof · cited by 3,593
- Bracket.bracketstatement and proof · cited by 642
- commutatorElementstatement · cited by 41
- Subgroup.closure_leproof · cited by 31
Cited by10
Results whose statement or proof uses this declaration.
- Subgroup.commutator_monoproof · cited by 11
- Subgroup.commutator_eq_bot_iff_le_centralizerproof · cited by 5
- Subgroup.commutator_le_rightproof · cited by 4
- Subgroup.commutator_pi_pi_leproof · cited by 2
- Subgroup.commutator_top_left_le_iffproof · cited by 2
- Subgroup.le_normalizer_iff_commutator_le_rightproof · cited by 1
- Subgroup.commutator_prod_prodproof · cited by 1
- IsPGroup.commutator_eq_bot_or_commutator_eq_selfproof · cited by 1
- Subgroup.commutator_comm_leproof · cited by 1
- Subgroup.commutator_le_supproof · cited by 0