Question: (2) Consider the polynomial f(x) = x 5 Q and let E = Q(i, V5) be its splitting field /Q. (a) Show that |GL(E/Q)|=

(2) Consider the polynomial f(x) = x4 – 5 € Q and let E = Qli, 15) be its splitting field /Q. (a) Show that GL(E/Q)] = [E:Q]

(2) Consider the polynomial f(x) = x 5 Q and let E = Q(i, V5) be its splitting field /Q. (a) Show that |GL(E/Q)|= [E: Q] = 8. (b) Describe all the automorphisms {01,...,os} in GL(E/Q). (c) Write the multiplication table for the group GL(E/Q). (d) Which finite group is GL(E/Q) isomorphic to? Hint: there are only two non-abelian finite grous of order 8 upto isomorphism. %3D

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