With \(\alpha =\sqrt {6+\sqrt {11}}\), prove that the extension \(\mathbb {Q}[\alpha ]/\mathbb {Q}\) is Galois and compute its Galois group.
Question
Math 6310 • Algebra
Spring 2020 • Question 7
Question
Spring 2020 • Question 7
With \(\alpha =\sqrt {6+\sqrt {11}}\), prove that the extension \(\mathbb {Q}[\alpha ]/\mathbb {Q}\) is Galois and compute its Galois group.