Theorems · Theorem · group theory
Subgroup.normalizerMonoidHom_ker
∀ {G : Type u_1} [inst : Group G] (H : Subgroup G),
H.normalizerMonoidHom.ker = (Subgroup.centralizer ↑H).subgroupOf (Subgroup.normalizer ↑H)- Defined in
- Mathlib.GroupTheory.Subgroup.Centralizer
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 28 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- MonoidHom.kerstatement · cited by 212
- MulAutstatement · cited by 158
- Subgroup.subgroupOfstatement · cited by 122
- Subgroup.normalizerstatement and proof · cited by 108
- Subgroup.centralizerstatement · cited by 65
- Subgroup.normalizerMonoidHomstatement · cited by 10
- Subgroup.normalizerMonoidHom_apply_apply_coeproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- IsCyclic.normalizer_le_centralizerproof · cited by 2
- IsZGroup.isCyclic_commutatorproof · cited by 1