Theorems · Theorem · group theory
Subgroup.normalCore_eq_ker
∀ {G : Type u_1} [inst : Group G] (H : Subgroup G), H.normalCore = (MulAction.toPermHom G (G ⧸ H)).ker- Defined in
- Mathlib.GroupTheory.GroupAction.Quotient
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 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.
Cites21
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
- mul_oneproof · cited by 3,885
- Subgroupstatement and proof · cited by 3,593
- HasQuotient.Quotientstatement and proof · cited by 2,301
- le_antisymmproof · cited by 2,068
- Equiv.Permstatement · cited by 1,375
- inv_invproof · cited by 494
- smul_eq_mulproof · cited by 357
- mul_inv_revproof · cited by 270
- MonoidHom.kerstatement and proof · cited by 212
- QuotientGroup.mkproof · cited by 196
- Equiv.Perm.extproof · cited by 75
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.normal_of_index_eq_minFac_cardproof · cited by 0