Theorems · Theorem · group theory
addCommutatorElement_def
∀ {G : Type u_1} [inst : AddGroup G] (g₁ g₂ : G), ⁅g₁, g₂⁆ = g₁ + g₂ + -g₁ + -g₂- Defined in
- Mathlib.Algebra.Group.Commutator
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- Bracket.bracketstatement · cited by 642
- addCommutatorElementstatement · cited by 35
Cited by8
Results whose statement or proof uses this declaration.
- AddSubgroup.upperCentralSeries_oneproof · cited by 4
- addCommutatorElement_eq_zero_iff_add_commproof · cited by 3
- AddSubgroup.upperCentralSeries_monoproof · cited by 3
- AddSubgroup.lowerCentralSeries_succ_eq_botproof · cited by 2
- AddSubgroup.Normal.quotient_commutative_iff_addCommutator_leproof · cited by 1
- AddSubgroup.upperCentralSeriesStep_eq_comap_centerproof · cited by 1
- AddSubgroup.mem_centralizer_iff_addCommutator_eq_zero'proof · cited by 0
- mem_addCommutatorSet_of_isAddConj_sqproof · cited by 0