Theorems · Theorem · group theory
Subgroup.Normal.quotient_commutative_iff_commutator_le
∀ {G : Type u_1} [inst : Group G] {N : Subgroup G} [inst_1 : N.Normal], IsMulCommutative (G ⧸ N) ↔ commutator G ≤ N- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupSubgroup.Normal
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Bracket.bracketproof · cited by 642
- Subgroup.Normalstatement and proof · cited by 334
- SetLike.mem_coeproof · cited by 302
- QuotientGroup.mkproof · cited by 196
- IsMulCommutativestatement and proof · cited by 95
- QuotientGroup.mk'proof · cited by 90
- commutatorstatement and proof · cited by 56
- Subgroup.subset_closureproof · cited by 53
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.Normal.commutator_le_of_self_sup_commutative_eq_topproof · cited by 1
- alternatingGroup.kleinFour_eq_commutatorproof · cited by 0