## Galois Group

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.

See also Abhyankar's Conjecture, Finite Group, Group

References

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

© 1996-9 Eric W. Weisstein
1999-05-25