Theorems · Theorem · group theory
Subgroup.mem_set_normalizer_iff
∀ {G : Type u_1} [inst : Group G] {S : Set G} {g : G}, g ∈ Subgroup.normalizer S ↔ ∀ (h : G), h ∈ S ↔ g * h * g⁻¹ ∈ 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
- Group
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
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- Subgroup.normalizerstatement · cited by 108
Cited by3
Results whose statement or proof uses this declaration.
- Subgroup.mem_normalizer_iffproof · cited by 1
- Sylow.smul_eq_iff_mem_normalizerproof · cited by 1
- Subgroup.mem_set_normalizer_iff''proof · cited by 1