Theorems · Theorem · group theory
Commute.commutator_eq
∀ {G : Type u_1} [inst : Group G] {g₁ g₂ : G}, Commute g₁ g₂ → ⁅g₁, g₂⁆ = 1- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext
- 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
- Bracket.bracketstatement · cited by 642
- Commutestatement and proof · cited by 639
- commutatorElementstatement · cited by 41
- commutatorElement_eq_one_iff_commuteproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- commutatorElement_one_leftproof · cited by 1
- commutatorElement_selfproof · cited by 1
- commutatorElement_one_rightproof · cited by 0