Theorems · Definition · group theory
AddSubgroup.index
{G : Type u_1} → [inst : AddGroup G] → AddSubgroup G → ℕThe index of an additive subgroup as a natural number. Returns 0 if the index is infinite. [Wikidata Q1464168](https://www.wikidata.org/wiki/Q1464168)
- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 104 results in Mathlib
- Foundations
- Depth 90 from the axioms, rests on 2,534 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
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.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- HasQuotient.Quotientproof · cited by 2,301
- Nat.cardproof · cited by 844
Cited by109
Results whose statement or proof uses this declaration.
- AddSubgroup.relIndexproof · cited by 67
- Submodule.cardQuotproof · cited by 14
- AddSubgroup.relIndex_mul_indexstatement and proof · cited by 12
- AddSubgroup.FiniteIndex.index_ne_zerostatement · cited by 10
- AddSubgroup.index_topstatement · cited by 9
- AddSubgroup.card_mul_indexstatement and proof · cited by 7
- AddSubgroup.relIndex_comapproof · cited by 7
- AddSubgroup.relIndex_top_rightstatement · cited by 7
- Ideal.absNorm_memproof · cited by 5
- AddSubgroup.index_eq_two_iffstatement · cited by 5
- AddSubgroup.inf_relIndex_rightproof · cited by 5
- AddSubgroup.finiteIndex_iffstatement and proof · cited by 4