Theorems · Definition · group theory
Subgroup.fintypeOfIndexNeZero
{G : Type u_1} → [inst : Group G] → {H : Subgroup G} → H.index ≠ 0 → Fintype (G ⧸ H)Finite index implies finite quotient.
- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 97 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.
Cites6
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 and proof · cited by 2,301
- Fintype.ofFiniteproof · cited by 255
- Subgroup.indexstatement and proof · cited by 150
Cited by5
Results whose statement or proof uses this declaration.
- Subgroup.fintypeQuotientOfFiniteIndexproof · cited by 9
- Subgroup.exists_pow_mem_of_index_ne_zeroproof · cited by 2
- MonoidHom.transfer_eq_pow_auxproof · cited by 2
- Subgroup.pairwiseDisjoint_leftCoset_cover_const_of_index_eqproof · cited by 1
- Subgroup.finite_quotient_of_finite_quotient_of_index_ne_zeroproof · cited by 1