Theorems · Definition · group theory
AddSubgroup.relIndex
{G : Type u_1} → [inst : AddGroup G] → AddSubgroup G → AddSubgroup G → ℕIf H and K are subgroups of an additive 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
- 67 results in Mathlib
- Foundations
- Depth 91 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.
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
- AddSubgroup.indexproof · cited by 104
- AddSubgroup.addSubgroupOfproof · cited by 87
Cited by70
Results whose statement or proof uses this declaration.
- AddSubgroup.relIndex_mul_indexstatement and proof · cited by 12
- AddSubgroup.Commensurableproof · cited by 8
- AddSubgroup.card_mul_indexproof · cited by 7
- AddSubgroup.relIndex_comapstatement and proof · cited by 7
- AddSubgroup.relIndex_top_rightstatement and proof · cited by 7
- AddSubgroup.inf_relIndex_rightstatement and proof · cited by 5
- AddSubgroup.relIndex_eq_zero_of_le_rightstatement and proof · cited by 5
- NumberField.absNorm_differentIdealproof · cited by 4
- AddAction.IsBlock.ncard_block_add_ncard_orbit_eqproof · cited by 4
- AddSubgroup.index_comapstatement · cited by 4
- AddSubgroup.relIndex_bot_leftstatement · cited by 4
- AddSubgroup.isFiniteRelIndex_iff_relIndex_ne_zerostatement · cited by 3