Theorems · Theorem · number theory
IsCyclotomicExtension.Rat.card_subgroupGalEquivSubgroupChar
∀ (n : ℕ) [inst : NeZero n] (K : Type u_1) [inst_1 : Field K] [inst_2 : NumberField K]
[hK : IsCyclotomicExtension {n} ℚ K] (R : Type u_2) [inst_3 : CommRing R]
[inst_4 : HasEnoughRootsOfUnity R (Monoid.exponent (ZMod n)ˣ)] [IsMulCommutative Gal(K/ℚ)] (H : Subgroup Gal(K/ℚ)),
Nat.card ↥(OrderDual.ofDual ((IsCyclotomicExtension.Rat.subgroupGalEquivSubgroupChar n K R) H)) =
Nat.card (Gal(K/ℚ) ⧸ H)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 218 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Equivstatement · cited by 8,337
- Fieldstatement and proof · cited by 7,404
- Subgroupstatement and proof · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- HasQuotient.Quotientstatement and proof · cited by 2,301
- AlgEquivstatement and proof · cited by 1,681
- ZModstatement and proof · cited by 1,024
- OrderDualstatement and proof · cited by 927
- OrderIsostatement and proof · cited by 874
Cited by1
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.Rat.card_intermediateFieldEquivSubgroupCharproof · cited by 0