Theorems · Theorem · group theory
charP_of_prime_pow_injective
∀ (R : Type u_6) [inst : Ring R] [inst_1 : Fintype R] (p n : ℕ) [hp : Fact (Nat.Prime p)], Fintype.card R = p ^ n → (∀ i ≤ n, ↑p ^ i = 0 → i = n) → CharP R (p ^ n)
- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Ringstatement and proof · cited by 7,463
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- Fintype.cardstatement and proof · cited by 1,386
- CharPstatement and proof · cited by 478
- CharP.cast_eq_zeroproof · cited by 357
- Fact.outproof · cited by 328
- Nat.cast_powproof · cited by 131
- CharP.cast_eq_zero_iffproof · cited by 42
- CharP.existsproof · cited by 16
- Nat.dvd_prime_powproof · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- TruncatedWittVector.charP_zmodproof · cited by 1