Theorems · Definition · group theory
Subgroup.fintypeQuotientOfFiniteIndex
{G : Type u_1} → [inst : Group G] → {H : Subgroup G} → [H.FiniteIndex] → Fintype (G ⧸ H)A finite index subgroup has finite quotient.
- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupSubgroup.FiniteIndex
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement · cited by 7,736
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- HasQuotient.Quotientstatement · cited by 2,301
- Subgroup.FiniteIndexstatement and proof · cited by 113
- Subgroup.FiniteIndex.index_ne_zeroproof · cited by 12
- Subgroup.fintypeOfIndexNeZeroproof · cited by 4
Cited by10
Results whose statement or proof uses this declaration.
- Subgroup.leftTransversals.diffproof · cited by 8
- Subgroup.smul_diff'proof · cited by 2
- Rep.coindToInd_applystatement · cited by 2
- MonoidHom.transfer_eq_powproof · cited by 2
- MonoidHom.transfer_eq_prod_quotient_orbitRel_zpowers_quotproof · cited by 2
- Subgroup.leftTransversals.smul_diff_smulproof · cited by 1
- ProperlyDiscontinuousSMul.ofFiniteRelIndexproof · cited by 1
- Subgroup.exists_finset_card_le_mulproof · cited by 1
- ModularGroup.exists_bound_of_subgroup_invariant_of_isBigOproof · cited by 1
- Subgroup.smul_diff_smul'proof · cited by 0