Theorems · Theorem · group theory
Subgroup.mem_normalizer_iff_map_conj_eq
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G} {g : G},
g ∈ Subgroup.normalizer ↑H ↔ Subgroup.map (↑(MulAut.conj g)) H = H- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- SetLike.coestatement · cited by 8,199
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- Subgroup.mapstatement · cited by 301
- MonoidHomClass.toMonoidHomstatement · cited by 294
- MulAutstatement · cited by 158
- Subgroup.normalizerstatement · cited by 108
- SetLike.ext'_iffproof · cited by 78
- MulAut.conjstatement · cited by 64
- Subgroup.mem_normalizer_iff_conj_image_eqproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Subgroup.le_normalizer_mapproof · cited by 4
- Subgroup.le_normalizer_closure_iffproof · cited by 1
- Subgroup.normalizer_le_normalizer_closureproof · cited by 0