Theorems · Theorem · group theory
Subgroup.mem_normalizer_iff_conj_image_eq
∀ {G : Type u_1} [inst : Group G] {s : Set G} {g : G}, g ∈ Subgroup.normalizer s ↔ ⇑(MulAut.conj g) '' s = s- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Setstatement and proof · cited by 53,352
- Groupstatement and proof · cited by 6,238
- Set.imagestatement and proof · cited by 5,609
- MonoidHomstatement · cited by 3,629
- Subgroupstatement · cited by 3,593
- MulEquivstatement · cited by 1,142
- MulAutstatement · cited by 158
- Subgroup.normalizerstatement · cited by 108
- MulAut.conjstatement and proof · cited by 64
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.mem_normalizer_iff_map_conj_eqproof · cited by 3
- Subgroup.normalizer_le_normalizer_closureproof · cited by 0