a. Show that automorphism
of a splitting field E over F of a polynomial f(x) ∈ F[x] permutes the zeros
o. 

b. Show that an automorphism of a splitting field E over F of a polynomial f(x) = ∈ F[x] is completely determined by the permutation of the zeros of f(x) in E given in part (a). 

c. Show that if E is a splitting field over F of a polynomial f(x) = ∈ F[x], then G(E/F) can be viewed in a
natural way as a certain group of permutations.