Theorems · Theorem · group theory
Subgroup.le_normalizer_comap
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G} {N : Type u_5} [inst_1 : Group N] (f : N →* G),
Subgroup.comap f (Subgroup.normalizer ↑H) ≤ Subgroup.normalizer ↑(Subgroup.comap f H)The preimage of the normalizer is contained in the normalizer of the preimage.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- SetLike.coestatement · cited by 8,199
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- map_mulproof · cited by 1,137
- Subgroup.comapstatement · cited by 154
- Subgroup.normalizerstatement · cited by 108
- map_invproof · cited by 95
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.comap_normalizer_eq_of_le_rangeproof · cited by 2
- Subgroup.IsSubnormal.comapproof · cited by 1