Theorems · Theorem · group theory
Subgroup.card_eq_card_quotient_mul_card_subgroup
∀ {α : Type u_1} [inst : Group α] (s : Subgroup α), Nat.card α = Nat.card (α ⧸ s) * Nat.card ↥s- Defined in
- Mathlib.GroupTheory.Coset.Card
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 94 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.
Cites7
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
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Nat.cardstatement and proof · cited by 844
- Nat.card_congrproof · cited by 133
- Nat.card_prodproof · cited by 24
- Subgroup.groupEquivQuotientProdSubgroupproof · cited by 4
Cited by8
Results whose statement or proof uses this declaration.
- Subgroup.card_subgroup_dvd_cardproof · cited by 8
- MonoidHom.domRestrict_surjectiveproof · cited by 2
- IsPGroup.isNilpotentproof · cited by 1
- Sylow.card_normalizer_modEq_cardproof · cited by 1
- Subgroup.card_quotient_dvd_cardproof · cited by 0
- Sylow.prime_dvd_card_quotient_normalizerproof · cited by 0
- alternatingGroup.kleinFour_eq_commutatorproof · cited by 0
- Sylow.exists_subgroup_card_pow_succproof · cited by 0