Theorems · Theorem · group theory
Subgroup.finiteIndex_iff
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G}, H.FiniteIndex ↔ H.index ≠ 0- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 92 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.
Cites5
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.indexstatement and proof · cited by 150
- Subgroup.FiniteIndexstatement and proof · cited by 113
- Subgroup.FiniteIndex.index_ne_zeroproof · cited by 12
Cited by5
Results whose statement or proof uses this declaration.
- Subgroup.isFiniteRelIndex_iff_finiteIndexproof · cited by 2
- NumberField.Units.finiteIndex_iff_sup_torsion_finiteIndexproof · cited by 2
- NumberField.Units.regOfFamily_div_regOfFamilyproof · cited by 1
- NumberField.Units.isMaxRank_iff_closure_finiteIndexproof · cited by 1
- Subgroup.isFiniteRelIndex_top_iffproof · cited by 0