Theorems · Theorem · group theory
Subgroup.normal_iff_map_conj_eq
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G}, H.Normal ↔ ∀ (g : G), Subgroup.map (↑(MulAut.conj g)) H = H- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 71 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- SetLike.coeproof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- Subgroup.Normalstatement · cited by 334
- Subgroup.mapstatement and proof · cited by 301
- MonoidHomClass.toMonoidHomstatement and proof · cited by 294
- MulAutstatement · cited by 158
- Subgroup.normalizerproof · cited by 108
- MulAut.conjstatement and proof · cited by 64
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.normalCore_eq_iInf_map_conjproof · cited by 1
- Subgroup.Normal.map_conj_eqproof · cited by 1