Theorems · Theorem · group theory
Subgroup.index_map_dvd
∀ {G : Type u_1} {G' : Type u_2} [inst : Group G] [inst_1 : Group G'] (H : Subgroup G) {f : G →* G'},
Function.Surjective ⇑f → (Subgroup.map f H).index ∣ H.index- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Groupstatement and proof · cited by 6,238
- mul_oneproof · cited by 3,885
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- Subgroup.mapstatement · cited by 301
- le_sup_leftproof · cited by 265
- MonoidHom.kerproof · cited by 212
- Subgroup.indexstatement and proof · cited by 150
- Subgroup.index_topproof · cited by 10
- Subgroup.index_dvd_of_leproof · cited by 8
- MonoidHom.range_eq_top_of_surjectiveproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- Sylow.mapSurjective_surjectiveproof · cited by 2
- Subgroup.index_map_eqproof · cited by 1