Theorems · Theorem · group theory
AddSubgroup.Normal.quotient_commutative_iff_addCommutator_le
∀ {G : Type u_1} [inst : AddGroup G] {N : AddSubgroup G} [inst_1 : N.Normal],
IsAddCommutative (G ⧸ N) ↔ addCommutator G ≤ N- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroupAddSubgroup.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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Bracket.bracketproof · cited by 642
- QuotientAddGroup.mkproof · cited by 348
- SetLike.mem_coeproof · cited by 302
- AddSubgroup.Normalstatement and proof · cited by 183
- QuotientAddGroup.mk'proof · cited by 60
- AddSubgroup.subset_closureproof · cited by 49
- IsAddCommutativestatement and proof · cited by 40
- QuotientAddGroup.eq_zero_iffproof · cited by 19
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.Normal.addCommutator_le_of_self_sup_commutative_eq_topproof · cited by 0