Theorems · Theorem · group theory
Subgroup.commutator_comm
∀ {G : Type u_1} [inst : Group G] (H₁ H₂ : Subgroup G), ⁅H₁, H₂⁆ = ⁅H₂, H₁⁆- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 72 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.
Cites5
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
- Subgroupstatement and proof · cited by 3,593
- le_antisymmproof · cited by 2,068
- Bracket.bracketstatement · cited by 642
- Subgroup.commutator_comm_leproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- Subgroup.commutator_le_leftproof · cited by 2
- Subgroup.le_normalizer_iff_commutator_le_leftproof · cited by 1
- Subgroup.normalizer_commutator_ge_rightproof · cited by 1
- Group.IsPerfect.upperCentralSeries_eq_centerproof · cited by 1
- Subgroup.commutator_top_left_eq_bot_iff_le_centerproof · cited by 0
- Subgroup.commutator_top_right_le_iffproof · cited by 0
- commutator_centralizer_commutator_le_centerproof · cited by 0