Theorems · Theorem · group theory
Subgroup.card_mul_index
∀ {G : Type u_1} [inst : Group G] (H : Subgroup G), Nat.card ↥H * H.index = Nat.card G- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 96 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.
Cites10
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
- Bot.botproof · cited by 4,720
- Subgroupstatement and proof · cited by 3,593
- Nat.cardstatement and proof · cited by 844
- bot_leproof · cited by 306
- Subgroup.indexstatement and proof · cited by 150
- Subgroup.relIndexproof · cited by 72
- Subgroup.relIndex_mul_indexproof · cited by 14
- Subgroup.relIndex_bot_leftproof · cited by 4
- Subgroup.index_botproof · cited by 2
Cited by16
Results whose statement or proof uses this declaration.
- Subgroup.index_mul_cardproof · cited by 7
- Subgroup.card_dvd_of_surjectiveproof · cited by 3
- Subgroup.exists_right_complement'_of_coprimeproof · cited by 2
- MonoidHom.surjective_of_card_ker_le_divproof · cited by 2
- Equiv.Perm.nat_card_centralizerproof · cited by 2
- Ideal.card_stabilizer_eq_card_inertia_mul_finrankproof · cited by 2
- IsPGroup.le_or_disjoint_of_coprimeproof · cited by 1
- Subgroup.commProb_quotient_leproof · cited by 1
- IsCyclic.card_powMonoidHom_kerproof · cited by 1
- Subgroup.card_commutator_dvd_index_center_powproof · cited by 1
- Subgroup.finite_iff_finite_and_finiteIndexproof · cited by 1
- Group.isCyclic_of_coprime_card_range_card_kerproof · cited by 1