Theorems · Theorem · field theory

gal_X_pow_sub_C_isSolvable_aux

∀ {F : Type u_1} [inst : Field F] (n : ℕ) (a : F),
  (Polynomial.map (RingHom.id F) (Polynomial.X ^ n - 1)).Splits →
    Group.IsSolvable (Polynomial.X ^ n - Polynomial.C a).Gal

Defined in: Mathlib.FieldTheory.AbelRuffini
Cited by: 1 results in Mathlib
Foundations: Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field

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Cites54

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
RingHom.idstatement and proof · cited by 18,349
RingHomstatement · cited by 10,189
Fieldstatement and proof · cited by 7,404
Polynomialstatement and proof · cited by 5,681
Algebra.algebraMapproof · cited by 4,706
mul_commproof · cited by 2,262
mul_assocproof · cited by 1,667
Polynomial.Xstatement and proof · cited by 1,639
Polynomial.Cstatement and proof · cited by 1,598
map_mulproof · cited by 1,137
pow_zeroproof · cited by 1,094

Cited by1

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gal_X_pow_sub_C_isSolvableproof · cited by 0