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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2007 • Question 8

Question

Math 6310 • Algebra Fall 2007 • Question 8

Compute the Galois group \(G(E/F)\) where \(E\) is the splitting field of the polynomial \(x^3-2\) and \(F\) is

  1. \(\mathbb {Q}\)
  2. \(\mathbb {R}\)
  3. \(\mathbb {F}_5\)
  4. \(\mathbb {F}_7\)

Raw LaTeX

Compute the Galois group \(G(E/F)\) where \(E\) is the splitting field of the polynomial
\(x^3-2\) and \(F\) is
\begin{enumerate}
\item[(1)] \(\mathbb{Q}\)
\item[(2)] \(\mathbb{R}\)
\item[(3)] \(\mathbb{F}_5\)
\item[(4)] \(\mathbb{F}_7\)
\end{enumerate}

Topic Tags

Finite Fields Galois Groups of Polynomials Galois Theory Splitting Fields