Theorems · Theorem · field theory

IntermediateField.map_fixingSubgroup_index

∀ {F : Type u_1} {E : Type u_2} (E' : Type u_3) [inst : Field F] [inst_1 : Field E] [inst_2 : Field E']
  [inst_3 : Algebra F E] [inst_4 : Algebra F E'] [inst_5 : Algebra E E'] [inst_6 : IsScalarTower F E E']
  (L : IntermediateField F E) [Normal F E] [Normal F E'],
  (IntermediateField.map (IsScalarTower.toAlgHom F E E') L).fixingSubgroup.index = L.fixingSubgroup.index

If K / E / k is a field extension tower with E / k and K / k normal, L is an intermediate field of E / k, then the index of the fixing subgroup of L viewed as an intermediate field of K / k is equal to the index of the fixing subgroup of L viewed as an intermediate field of E / k.

Defined in

Mathlib.FieldTheory.Galois.Basic

Cited by

1 results in Mathlib

Foundations

Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFieldFieldAlgebraAlgebraAlgebraIsScalarTowerNormalNormal