Theorems · Theorem · group theory
AddSubgroup.finiteIndex_iff_finite_quotient
∀ {G : Type u_1} [inst : AddGroup G] {H : AddSubgroup G}, H.FiniteIndex ↔ Finite (G ⧸ H)- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
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.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- Finitestatement and proof · cited by 3,029
- HasQuotient.Quotientstatement and proof · cited by 2,301
- AddSubgroup.FiniteIndexstatement and proof · cited by 66
- AddSubgroup.finiteIndex_of_finite_quotientproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.finiteIndex_range_nsmulAddMonoidHom_of_fgproof · cited by 1
- AddMonoidHom.finite_iff_finite_ker_rangeproof · cited by 1