Theorems · Definition · group theory
Abelianization
(G : Type u) → [Group G] → Type u
The abelianization of G is the quotient of G by its commutator subgroup.
- Defined in
- Mathlib.GroupTheory.Abelianization.Defs
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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.
- Groupstatement and proof · cited by 6,238
- HasQuotient.Quotientproof · cited by 2,301
- commutatorproof · cited by 56
Cited by42
Results whose statement or proof uses this declaration.
- FreeAbelianGroupproof · cited by 82
- Abelianization.ofstatement · cited by 20
- Abelianization.liftstatement and proof · cited by 9
- Abelianization.mapstatement · cited by 5
- groupHomology.H1AddEquivOfIsTrivialstatement · cited by 4
- MulEquiv.abelianizationCongrstatement · cited by 4
- Abelianization.hom_extstatement and proof · cited by 4
- groupHomology.H1ToTensorOfIsTrivialstatement and proof · cited by 3
- groupHomology.mkH1OfIsTrivialstatement · cited by 3
- Abelianization.equivOfCommstatement and proof · cited by 2
- groupHomology.H1AddEquivOfIsTrivial_applystatement · cited by 1
- groupHomology.H1ToTensorOfIsTrivial_H1π_singlestatement and proof · cited by 1