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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2005 • Question 9

Question

Math 6310 • Algebra Spring 2005 • Question 9

Let \(G_F\) denote the Galois group of \(x^3-3x^2-3\) over the field \(F\). Determine \(G_F\) when:

  1. \(F\) is the complex numbers;
  2. \(F\) is the real numbers;
  3. \(F\) is the rational numbers; and
  4. \(F\) is the integers modulo 2.

Raw LaTeX

Let \(G_F\) denote the Galois group of \(x^3-3x^2-3\) over the field \(F\). Determine \(G_F\) when:
\begin{enumerate}
\item[(a)] \(F\) is the complex numbers;
\item[(b)] \(F\) is the real numbers;
\item[(c)] \(F\) is the rational numbers; and
\item[(d)] \(F\) is the integers modulo 2.
\end{enumerate}

Topic Tags

Chinese Remainder Theorem and Product Decompositions Galois Theory