Suppose is the Galois Group over of one of the polynomials:
For your choice of polynomial, find the generators of the splitting field over and describe the elements of G by their effect on these generators. Finally, describe the group by generators and relations.
I just need to do one of the polynomials above and I am just beginning to learn Galois Theory, so I don't understand how to do this. I guess I need a good head start on how to solve this problem. Thanks.