Theorems · Theorem · group theory
Abelianization.commutator_subset_ker
∀ {G : Type u} [inst : Group G] {A : Type v} [inst_1 : CommGroup A] (f : G →* A), commutator G ≤ f.ker- Defined in
- Mathlib.GroupTheory.Abelianization.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- one_mulproof · cited by 2,841
- map_mulproof · cited by 1,137
- CommGroupstatement and proof · cited by 990
- Bracket.bracketproof · cited by 642
- MonoidHom.kerstatement and proof · cited by 212
- mul_inv_cancelproof · cited by 128
- mul_right_commproof · cited by 108
- map_invproof · cited by 95
Cited by5
Results whose statement or proof uses this declaration.
- Sylow.not_dvd_card_commutator_or_not_dvd_index_commutatorproof · cited by 1
- Subgroup.card_commutator_dvd_index_center_powproof · cited by 1
- IsZGroup.isCyclic_commutatorproof · cited by 1
- IsZGroup.commutator_ltproof · cited by 0
- Subgroup.commutator_inf_eq_focalSubgroupproof · cited by 0