Question

I really don’t understand number three. I know why it is irreducible. But I don’t know how to do the rest of it. And since I can’t do three I can’t do four. And since I can’t before I cant do five. help me please.

Show that QV2): Q1 3. (We ve looked at uus previoes 2. [Q(Vz, 3): Q(V2)] = 2. Q(2) and use it to show that Explain why x2 +3 is irreducible over 3. Then, apply the tower theorem to find [Q(V2, iv3): Q}. Use (3) to explain why the Galois group, I(Q(V2, ivV3): Q) has six elements. Find the elements of the Galois Group (they are automorphisms of Q(V2, iv3): Q that leave Q fixed; i.e., that are permutations of the three cube roots of two). 4. Make a group table of the Galois group. 5.

Answer 1

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