Theorems · Theorem · field theory
gal_isSolvable_of_splits
∀ {F : Type u_1} [inst : Field F] {p q : Polynomial F},
Fact (Polynomial.map (algebraMap F q.SplittingField) p).Splits → Group.IsSolvable q.Gal → Group.IsSolvable p.Gal- Defined in
- Mathlib.FieldTheory.AbelRuffini
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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Cites11
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- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapstatement and proof · cited by 4,706
- Factstatement and proof · cited by 2,726
- Polynomial.mapstatement and proof · cited by 806
- Polynomial.Splitsstatement and proof · cited by 290
- Group.IsSolvablestatement and proof · cited by 46
- Polynomial.SplittingFieldstatement and proof · cited by 42
- Polynomial.Galstatement and proof · cited by 37
- AlgEquiv.restrictNormalHom_surjectiveproof · cited by 6
- Group.isSolvable_of_surjectiveproof · cited by 4
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