Theorems · Theorem · group theory
AddSubgroup.mem_normalizer_iff_addConj_image_eq
∀ {G : Type u_1} [inst : AddGroup G] {s : Set G} {g : G}, g ∈ AddSubgroup.normalizer s ↔ ⇑(AddAut.addConj g) '' s = s- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Set.imagestatement and proof · cited by 5,609
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- AddMonoidHomstatement · cited by 3,230
- AddEquivstatement · cited by 1,087
- add_assocproof · cited by 746
- Set.mem_imageproof · cited by 131
- Set.ext_iffproof · cited by 90
- AddAutstatement · cited by 75
- AddSubgroup.normalizerstatement · cited by 59
Cited by3
Results whose statement or proof uses this declaration.
- AddSubgroup.mem_normalizer_iff_map_addConj_eqproof · cited by 6
- AddSubgroup.normalizer_le_normalizer_closureproof · cited by 0
- AddSubgroup.mem_normalizer_iff_conj_image_eqproof · cited by 0