Let be a Field Extension of , denoted , and let be the set of Automorphisms of , that is, the set of Automorphisms of such that for every , so that is fixed. Then is a Group of transformations of , called the Galois group of .

The Galois group of consists of the Identity Element and Complex Conjugation. These functions both take a given Real to the same real.

**References**

Jacobson, N. *Basic Algebra I, 2nd ed.* New York: W. H. Freeman, p. 234, 1985.

© 1996-9

1999-05-25