Theorems · Theorem · number theory

IsPrimitiveRoot.finite_quotient_span_sub_one

∀ {p k : ℕ} {K : Type u} [inst : Field K] {ζ : K} [hp : Fact (Nat.Prime p)] [inst_1 : CharZero K]
  [hcycl : IsCyclotomicExtension {p ^ (k + 1)} ℚ K] (hζ : IsPrimitiveRoot ζ (p ^ (k + 1))),
  Finite (NumberField.RingOfIntegers K ⧸ Ideal.span {hζ.toInteger - 1})

Defined in

Mathlib.NumberTheory.NumberField.Cyclotomic.Basic

Cited by

1 results in Mathlib

Foundations

Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFactCharZeroIsCyclotomicExtension