Theorems · Theorem · group theory
commutatorElement_eq_one_iff_mul_comm
∀ {G : Type u_1} [inst : Group G] {g₁ g₂ : G}, ⁅g₁, g₂⁆ = 1 ↔ g₁ * g₂ = g₂ * g₁- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- commutatorElementstatement · cited by 41
- mul_inv_eq_oneproof · cited by 20
- mul_inv_eq_iff_eq_mulproof · cited by 13
- commutatorElement_defproof · cited by 10
Cited by3
Results whose statement or proof uses this declaration.
- Subgroup.commutator_eq_bot_iff_le_centralizerproof · cited by 5
- Subgroup.Normal.quotient_commutative_iff_commutator_leproof · cited by 2
- commutatorElement_eq_one_iff_commuteproof · cited by 1