Theorems · Theorem · field theory

IsGaloisGroup.card_eq_finrank

∀ (G : Type u_1) (K : Type u_3) (L : Type u_4) [inst : Group G] [inst_1 : Field K] [inst_2 : Field L]
  [inst_3 : Algebra K L] [inst_4 : MulSemiringAction G L] [IsGaloisGroup G K L], Nat.card G = Module.finrank K L

The cardinality of a Galois group equals the degree of the field extension. See IsGaloisGroup.card_eq_finrank' for a ring-theoretic generalization assuming finiteness.

Defined in

Mathlib.FieldTheory.Galois.IsGaloisGroup

Cited by

10 results in Mathlib

Foundations

Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupFieldFieldAlgebraMulSemiringActionIsGaloisGroup