Let f(x) = x3 - 2 ∈ ℚ[X] and let K ⊂ ℂ be the splitting field of f(X) over ℚ.
Let ω = e2πi/3. Which of the following statements are true?
1
The Galois group of K over ℚ is the symmetric group S3.
2
The Galois group of K over ℚ(ω) is the symmetric group S3.
3
The Galois group of K over ℚ is ℤ/3ℤ.
4
The Galois group of K over ℚ(ω) is ℤ/3ℤ.