Let \(L=\mathbb {Q}(e^{2\pi i/8})\). Determine all subgroups of the Galois group \(\operatorname {Gal}(L/\mathbb {Q})\), and the corresponding intermediate fields.
Question
Math 6310 • Algebra
Spring 2009 • Question 10
Question
Spring 2009 • Question 10
Let \(L=\mathbb {Q}(e^{2\pi i/8})\). Determine all subgroups of the Galois group \(\operatorname {Gal}(L/\mathbb {Q})\), and the corresponding intermediate fields.