Theorems · Theorem · number theory
FiniteField.card
∀ (K : Type u_1) [inst : Field K] [inst_1 : Fintype K] (p : ℕ) [CharP K p], ∃ n, Nat.Prime p ∧ Fintype.card K = p ^ ↑n
The cardinality q is a power of the characteristic of K.
- Defined in
- Mathlib.FieldTheory.Finite.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Moduleproof · cited by 20,661
- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Factproof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- Fintype.cardstatement and proof · cited by 1,386
- pow_zeroproof · cited by 1,094
- ZModproof · cited by 1,024
- CharPstatement and proof · cited by 478
- PNatstatement · cited by 392
- le_of_eqproof · cited by 366
- Fact.outproof · cited by 328
Cited by12
Results whose statement or proof uses this declaration.
- FiniteField.even_card_iff_char_twoproof · cited by 2
- FiniteField.expand_cardproof · cited by 2
- FiniteField.Matrix.charpoly_pow_cardproof · cited by 2
- Char.card_pow_cardproof · cited by 1
- FiniteField.two_pow_cardproof · cited by 1
- IsArithFrobAt.exists_of_isInvariantproof · cited by 1
- Ideal.exists_prime_and_absNorm_eq_powproof · cited by 1
- FiniteField.card'proof · cited by 1
- jacobiSum_mul_jacobiSum_invproof · cited by 0
- FiniteField.isSquare_odd_prime_iffproof · cited by 0
- FiniteField.algEquivOfCardEqproof · cited by 0
- FiniteField.ringEquivOfCardEqproof · cited by 0