Theorems · Theorem · group theory
AddSubgroup.mem_set_normalizer_iff
∀ {G : Type u_1} [inst : AddGroup G] {S : Set G} {g : G},
g ∈ AddSubgroup.normalizer S ↔ ∀ (h : G), h ∈ S ↔ g + h + -g ∈ S- Defined in
- Mathlib.Algebra.Group.Subgroup.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.normalizerstatement · cited by 59
Cited by3
Results whose statement or proof uses this declaration.
- AddSubgroup.mem_normalizer_iffproof · cited by 3
- AddSubgroup.mem_set_normalizer_iff''proof · cited by 2
- AddCommGroup.normalizer_eq_topproof · cited by 0