Theorems · Theorem · group theory
AddSubgroup.le_normalizer_comap
∀ {G : Type u_1} [inst : AddGroup G] {H : AddSubgroup G} {N : Type u_5} [inst_1 : AddGroup N] (f : N →+ G),
AddSubgroup.comap f (AddSubgroup.normalizer ↑H) ≤ AddSubgroup.normalizer ↑(AddSubgroup.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.
Cites11
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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- map_addproof · cited by 964
- map_negproof · cited by 378
- AddSubgroup.comapstatement · cited by 123
- AddSubgroup.normalizerstatement · cited by 59
- AddSubgroup.mem_comapproof · cited by 11
- AddSubgroup.mem_normalizer_iffproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.comap_normalizer_eq_of_le_rangeproof · cited by 2
- AddSubgroup.IsSubnormal.comapproof · cited by 1