![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() |
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.