Theorems · Definition · group theory
AddSubgroup.normalCore
{G : Type u_1} → [inst : AddGroup G] → AddSubgroup G → AddSubgroup GThe normal core of an additive subgroup H is the largest normal additive
subgroup of G contained in H, as shown by AddSubgroup.normalCore_eq_iSup.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext
- Assumes
- AddGroup
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.
- Set.ofPredproof · cited by 6,101
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
Cited by11
Results whose statement or proof uses this declaration.
- AddSubgroup.normalCore_lestatement and proof · cited by 7
- AddSubgroup.normal_le_normalCorestatement · cited by 4
- AddGroup.residuallyFinite_iff_forall_finiteIndexproof · cited by 1
- AddSubgroup.normalCore_eq_iInf_comap_addConjstatement and proof · cited by 1
- AddSubgroup.normalCore_eq_iInf_map_addConjstatement and proof · cited by 1
- AddSubgroup.normalCore_eq_selfstatement · cited by 1
- AddSubgroup.normalCore_isClosedstatement · cited by 1
- AddSubgroup.normalCore_eq_iSupstatement and proof · cited by 0
- AddSubgroup.normalCore_idempotentstatement and proof · cited by 0
- AddSubgroup.normalCore_monostatement · cited by 0