Theorems · Theorem · group theory
Subgroup.map_map
∀ {G : Type u_1} [inst : Group G] (K : Subgroup G) {N : Type u_5} [inst_1 : Group N] {P : Type u_6} [inst_2 : Group P]
(g : N →* P) (f : G →* N), Subgroup.map g (Subgroup.map f K) = Subgroup.map (g.comp f) K- Defined in
- Mathlib.Algebra.Group.Subgroup.Map
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 21 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.coeproof · 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
- MonoidHom.compstatement and proof · cited by 469
- SetLike.coe_injectiveproof · cited by 374
- Subgroup.mapstatement and proof · cited by 301
- Set.image_imageproof · cited by 140
Cited by7
Results whose statement or proof uses this declaration.
- MonoidHom.map_rangeproof · cited by 5
- Subgroup.le_normalizer_mapproof · cited by 4
- Subgroup.map_symm_eq_iff_map_eqproof · cited by 4
- Sylow.normalizer_sup_eq_topproof · cited by 2
- Subgroup.normalCore_eq_iInf_map_conjproof · cited by 1
- Subgroup.Normal.commutator_le_of_self_sup_commutative_eq_topproof · cited by 1
- Subgroup.commutator_prod_prodproof · cited by 1