Galois Group

Let $L$ be a Field Extension of $K$, denoted $L/K$, and let $G$ be the set of Automorphisms of $L/K$, that is, the set of Automorphisms $\sigma$ of $L$ such that $\sigma(x)=x$ for every $x\in K$, so that $K$ is fixed. Then $G$ is a Group of transformations of $L$, called the Galois group of $L/K$.

The Galois group of $(\Bbb{C}/\Bbb{R})$ 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.