Galois Theory Solutions: Patrick Morandi Field

: Using the language of Group Theory to describe the "shuffling" or symmetries of the roots of equations. Splitting Fields

Let ( K/F ) be a finite Galois extension with Galois group ( G ). Suppose ( H ) is a subgroup of ( G ). Prove that the fixed field ( K^H ) is the smallest subfield of ( K ) containing ( F ) that is Galois over ( F ) with Galois group ( G/H ) if and only if ( H ) is normal in ( G ). patrick morandi field galois theory solutions