First, the zero of are just the zeros of , excluding 1. If if is such a 0, then so that . The only 'hard' part is showin that is not 1 for n= 1, 2, ..., p-1. It is important that p is prime. here.

Suppose for i< j< p. Then . Show that that is impossible.

[tex](b) Show that is abelian of order .

(c) Show that the fixed field of is .

For (a), these are the nth roots of unity? For (b), consider two automorphisms of and show that they commute? For (c), isn't this by definition?[/QUOTE]