Theorems · Theorem · group theory
Subgroup.relIndex_comap_ne_zero
∀ {G : Type u_1} {G' : Type u_2} [inst : Group G] [inst_1 : Group G'] (f : G →* G') {J K : Subgroup G'},
J.relIndex K ≠ 0 → (Subgroup.comap f J).relIndex (Subgroup.comap f K) ≠ 0If J has finite index in K, then the same holds for their comaps under any group hom.
- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, 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.
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- Subgroup.mapproof · cited by 301
- Subgroup.comapstatement and proof · cited by 154
- Subgroup.relIndexstatement and proof · cited by 72
- Subgroup.relIndex_comapproof · cited by 7
- Subgroup.relIndex_eq_zero_of_le_rightproof · cited by 5
- Subgroup.map_comap_leproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.relIndex_inter_ne_zeroproof · cited by 0