Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Summer 2017 • Question 10

Question

Math 6310 • Algebra Summer 2017 • Question 10

Let \(E:=\mathbb {Q}(\zeta +\zeta ^{-1})\) where \(\zeta \in \mathbb {C}\) is a primitive \(n\)th root of 1, for some integer \(n\ge 3\). Determine the Galois group of \(E\) over \(\mathbb {Q}\).

Raw LaTeX

Let \(E:=\mathbb{Q}(\zeta+\zeta^{-1})\) where \(\zeta\in\mathbb{C}\) is a primitive \(n\)th root of
1, for some integer \(n\ge 3\). Determine the Galois group of \(E\) over \(\mathbb{Q}\).

Topic Tags

Cyclotomic Fields Galois Groups of Polynomials Galois Theory