Theorems · Theorem · group theory
map_commutatorElement
∀ {G : Type u_1} {G' : Type u_2} {F : Type u_3} [inst : Group G] [inst_1 : Group G'] [inst_2 : FunLike F G G']
[MonoidHomClass F G G'] (f : F) (g₁ g₂ : G), f ⁅g₁, g₂⁆ = ⁅f g₁, f g₂⁆- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Groupstatement and proof · cited by 6,238
- FunLikestatement and proof · cited by 2,560
- map_mulproof · cited by 1,137
- Bracket.bracketstatement · cited by 642
- MonoidHomClassstatement and proof · cited by 244
- map_invproof · cited by 95
- commutatorElementstatement · cited by 41
Cited by4
Results whose statement or proof uses this declaration.
- Subgroup.map_commutatorproof · cited by 12
- Subgroup.upperCentralSeries.mapproof · cited by 3
- Subgroup.Normal.quotient_commutative_iff_commutator_leproof · cited by 2
- alternatingGroup.commutator_perm_leproof · cited by 1