Theorems · Definition · number theory

galXPowEquivUnitsZMod

{n : ℕ} →
  [NeZero n] →
    {K : Type u_1} →
      [inst : Field K] →
        {L : Type u_2} →
          [inst_1 : Field L] →
            [inst_2 : Algebra K L] →
              [IsCyclotomicExtension {n} K L] →
                Irreducible (Polynomial.cyclotomic n K) → (Polynomial.X ^ n - 1).Gal ≃* (ZMod n)ˣ

IsCyclotomicExtension.autEquivPow repackaged in terms of Gal. Asserts that the Galois group of X ^ n - 1 is equivalent to (ZMod n)ˣ if cyclotomic n K is irreducible in the base field.

Defined in: Mathlib.NumberTheory.Cyclotomic.Gal
Cited by: 0 results in Mathlib
Foundations: Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NeZero Field Field Algebra IsCyclotomicExtension

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Setstatement · cited by 53,352
Algebrastatement and proof · cited by 11,388
Fieldstatement and proof · cited by 7,404
Polynomialstatement · cited by 5,681
Unitsstatement · cited by 2,804
Polynomial.Xstatement and proof · cited by 1,639
MulEquivstatement · cited by 1,142
ZModstatement · cited by 1,024
Irreduciblestatement and proof · cited by 496
MulEquiv.symmproof · cited by 482
IsCyclotomicExtensionstatement and proof · cited by 220
Polynomial.cyclotomicstatement and proof · cited by 130

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