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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2007 • Question 7

Question

Math 6310 • Algebra Fall 2007 • Question 7

Let \(\zeta _8=e^{\frac {\pi }{4}i}\). Determine the Galois group of \(K=\mathbb {Q}(\zeta _8)\) and then determine all quadratic extensions of \(\mathbb {Q}\) contained in \(K\).

Raw LaTeX

Let \(\zeta_8=e^{\frac{\pi}{4}i}\). Determine the Galois group of
\(K=\mathbb{Q}(\zeta_8)\) and then determine all quadratic extensions of \(\mathbb{Q}\)
contained in \(K\).

Topic Tags

Cyclotomic Fields Ext Functors and Module Extensions Galois Groups of Polynomials Galois Theory