Theorems · Definition · group theory
Subgroup.normalClosure
{G : Type u_1} → [inst : Group G] → Set G → Subgroup GThe normal closure of a set s is the subgroup closure of all the conjugates of
elements of s. It is the smallest normal subgroup containing s.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 35 results in Mathlib
- Foundations
- Depth 67 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.
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
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- Subgroup.closureproof · cited by 196
- Group.conjugatesOfSetproof · cited by 9
Cited by41
Results whose statement or proof uses this declaration.
- PresentedGroupproof · cited by 21
- Subgroup.normalClosure_le_normalstatement and proof · cited by 10
- Subgroup.IsFinitelyNormallyGeneratedproof · cited by 10
- Subgroup.subset_normalClosurestatement · cited by 9
- Subgroup.map_normalClosurestatement and proof · cited by 3
- PresentedGroup.toGroupproof · cited by 3
- CoxeterMatrix.reindexGroupEquivproof · cited by 3
- Subgroup.closure_le_normalClosurestatement and proof · cited by 3
- PresentedGroup.equivPresentedGroupproof · cited by 2
- Subgroup.normalClosure_eq_selfstatement · cited by 2
- Subgroup.normalClosure_subset_iffstatement · cited by 2
- Subgroup.le_normalClosurestatement · cited by 2