Theorems · Definition · field theory

IsGaloisGroup.mulEquivCongr

(G : Type u_1) →
  (G' : Type u_2) →
    [inst : Group G] →
      [inst_1 : Group G'] →
        (A : Type u_5) →
          (B : Type u_6) →
            [inst_2 : CommRing A] →
              [inst_3 : CommRing B] →
                [IsDomain B] →
                  [inst_5 : Algebra A B] →
                    [FaithfulSMul A B] →
                      [inst_7 : MulSemiringAction G B] →
                        [inst_8 : MulSemiringAction G' B] →
                          [IsGaloisGroup G A B] → [IsGaloisGroup G' A B] → [Finite G] → [Finite G'] → G ≃* G'

If G and G' are finite Galois groups for B/A, then G is isomorphic to G'.

Defined in

Mathlib.FieldTheory.Galois.IsGaloisGroup

Cited by

5 results in Mathlib

Foundations

Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupGroupCommRingCommRingIsDomainAlgebraFaithfulSMulMulSemiringActionMulSemiringActionIsGaloisGroupIsGaloisGroupFiniteFinite