Theorems · Theorem · group theory
AddSubgroup.normal_iff_map_addConj_eq
∀ {G : Type u_1} [inst : AddGroup G] {H : AddSubgroup G},
H.Normal ↔ ∀ (g : G), AddSubgroup.map (↑(AddAut.addConj g)) H = H- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddMonoidHomstatement · cited by 3,230
- AddMonoidHomClass.toAddMonoidHomstatement and proof · cited by 232
- AddSubgroup.mapstatement and proof · cited by 189
- AddSubgroup.Normalstatement · cited by 183
- AddAutstatement · cited by 75
- AddSubgroup.normalizerproof · cited by 59
- AddAut.addConjstatement and proof · cited by 34
- AddSubgroup.eq_top_iff'proof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.normalCore_eq_iInf_map_addConjproof · cited by 1
- AddSubgroup.Normal.map_addConj_eqproof · cited by 1