Field theory MOC Automorphism of a field extension Let be a field extension. An automorphism of is a field automorphism of fixing (the image of) pointwise, field i.e. In the case of a Galois extension, this is denoted and called the Galois group. An automorphism of a field extension is a special case of an Morphism of field extensions. Properties Bound on the automorphism group of a finite simple extension tidy | en | sembr