
Chapter 13
A Worked Example
The Fundamental Theorem of Galois theory is quite a lot to take in at one go, so it is
worth spending some time thinking it through. We therefore analyse how the Galois
correspondence works out on an extended example.
The extension that we discuss is a favourite with writers on Galois theory, because
of its archetypal quality. A simpler example would be too small to illustrate the theory
adequately, and anything more complicated would be unwieldy. The example is the
Galois group of the splitting field of t
4
−2 over Q.
The discussion will be cut into small pieces to make it more easily digestible.
(1) Let f (t) = t
4
−2 over Q