Theorems · Definition · group theory
Subgroup.relIndex
{G : Type u_1} → [inst : Group G] → Subgroup G → Subgroup G → ℕIf H and K are subgroups of a group G, then relIndex H K : ℕ is the index
of H ∩ K in K. The function returns 0 if the index is infinite.
- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 72 results in Mathlib
- Foundations
- Depth 91 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.
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.indexproof · cited by 150
- Subgroup.subgroupOfproof · cited by 122
Cited by75
Results whose statement or proof uses this declaration.
- Subgroup.Commensurableproof · cited by 20
- Subgroup.card_mul_indexproof · cited by 16
- Subgroup.relIndex_mul_indexstatement and proof · cited by 14
- Subgroup.index_dvd_of_leproof · cited by 8
- Subgroup.inf_relIndex_rightstatement and proof · cited by 8
- Subgroup.relIndex_comapstatement and proof · cited by 7
- Subgroup.relIndex_eq_onestatement · cited by 6
- Subgroup.relIndex_top_rightstatement and proof · cited by 6
- Subgroup.relIndex_eq_zero_of_le_rightstatement and proof · cited by 5
- Subgroup.relIndex_ne_zerostatement · cited by 5
- Subgroup.index_comapstatement · cited by 5
- Subgroup.relIndex_bot_leftstatement · cited by 4