Theorems · Definition · group theory
AddSubgroup.normalClosure
{G : Type u_1} → [inst : AddGroup G] → Set G → AddSubgroup GThe normal closure of a set s is the closure of all the additive conjugates of
elements of s. It is the smallest normal additive subgroup containing s.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- AddSubgroup.closureproof · cited by 156
- AddGroup.addConjugatesOfSetproof · cited by 9
Cited by22
Results whose statement or proof uses this declaration.
- AddSubgroup.normalClosure_le_normalstatement and proof · cited by 9
- AddSubgroup.IsFinitelyNormallyGeneratedproof · cited by 8
- AddSubgroup.subset_normalClosurestatement · cited by 7
- AddSubgroup.map_normalClosurestatement and proof · cited by 3
- AddSubgroup.closure_le_normalClosurestatement and proof · cited by 3
- AddSubgroup.normalClosure_eq_selfstatement · cited by 2
- addCommutator_eq_normalClosurestatement and proof · cited by 1
- AddSubgroup.comap_normalClosure_image_gestatement · cited by 1
- AddSubgroup.IsFinitelyNormallyGenerated.comapproof · cited by 1
- AddSubgroup.addCommutator_def'statement · cited by 1
- AddSubgroup.normalClosure_closure_eq_normalClosurestatement · cited by 1
- AddSubgroup.map_normalClosure_lestatement · cited by 1