Theorems · Theorem · group theory
Subgroup.isFiniteRelIndex_iff_finiteIndex
∀ {G : Type u_1} [inst : Group G] {H K : Subgroup G}, H.IsFiniteRelIndex K ↔ (H.subgroupOf K).FiniteIndex- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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
- Subgroupstatement and proof · cited by 3,593
- Subgroup.indexproof · cited by 150
- Subgroup.subgroupOfstatement and proof · cited by 122
- Subgroup.FiniteIndexstatement and proof · cited by 113
- Subgroup.relIndexproof · cited by 72
- Subgroup.IsFiniteRelIndexstatement · cited by 26
- Subgroup.finiteIndex_iffproof · cited by 5
- Subgroup.isFiniteRelIndex_iff_relIndex_ne_zeroproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.isFiniteRelIndex_of_le_leftproof · cited by 1
- Subgroup.isFiniteRelIndex_map_powMonoidHom_of_fgproof · cited by 0