Theorems · Theorem · group theory
Subgroup.FiniteIndex.index_ne_zero
∀ {G : Type u_1} {inst : Group G} {H : Subgroup G} [self : H.FiniteIndex], H.index ≠ 0The subgroup has finite index;
recall that Subgroup.index returns 0 when the index is infinite.
- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Subgroup.FiniteIndex
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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 · cited by 150
- Subgroup.FiniteIndexstatement and proof · cited by 113
Cited by13
Results whose statement or proof uses this declaration.
- Subgroup.fintypeQuotientOfFiniteIndexproof · cited by 9
- Subgroup.finiteIndex_iffproof · cited by 5
- Subgroup.leftCoset_cover_filter_FiniteIndex_auxproof · cited by 3
- Subgroup.finiteIndex_of_leproof · cited by 3
- Subgroup.index_antitoneproof · cited by 2
- NumberField.Units.finiteIndex_iff_sup_torsion_finiteIndexproof · cited by 2
- Subgroup.finiteIndex_iInfproof · cited by 2
- Subgroup.index_rangeproof · cited by 1
- Subgroup.finite_iff_finite_and_finiteIndexproof · cited by 1
- CongruenceSubgroup.finiteIndex_conjGLproof · cited by 0
- Subgroup.index_strictAntiproof · cited by 0
- CongruenceSubgroup.isArithmetic_conj_SL2Zproof · cited by 0