Hello.

I have to find a splitting field

of the polynomial

over

and the galois group and all intermediate fields of the algebraic extension

.

I found out, that

is irreducible, the roots of

are:

and that

is a splitting field of

.

Furthermore I find out, that the three homomorphisms

have order 2, so the galois group is isomorph to

.

But now I don't know how to find the fixed fields, which belongs to the homomorphisms.

For example: Which fixed field belongs to the homomorphism

?

The definition says:

...and this don't help me, because I need a description of the fixed field like this:

(with suitable

).

I hope, you can help me.

Bye,

Alex