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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2006 • Question 6

Question

Math 6310 • Algebra Spring 2006 • Question 6

Let \(G\) be the Galois group of the polynomial \(x^4-5\) over the field \(F\). Determine \(G\) in each of the following cases:

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

Raw LaTeX

Let \(G\) be the Galois group of the polynomial \(x^4-5\) over the field \(F\). Determine \(G\) in each
of the following cases:
\begin{enumerate}
\item[(a)] \(F\) is the real numbers;
\item[(b)] \(F\) is the rational numbers;
\item[(c)] \(F\) is the integers modulo 3.
\end{enumerate}

Topic Tags

Galois Groups of Polynomials Galois Theory Irreducible Polynomials Polynomial Rings and Ring Homomorphism Kernels