Theorems · Theorem · group theory
Subgroup.mem_normalizer_iff
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G} {g : G},
g ∈ Subgroup.normalizer ↑H ↔ ∀ (h : G), h ∈ H ↔ g * h * g⁻¹ ∈ H- Defined in
- Mathlib.Algebra.Group.Subgroup.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, 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.
- SetLike.coestatement · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Subgroup.normalizerstatement · cited by 108
- Subgroup.mem_set_normalizer_iffproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.coe_mul_of_left_le_normalizer_rightproof · cited by 2