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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6320 • Algebra II

Summer 2022 • Question 2

Question

Math 6320 • Algebra II Summer 2022 • Question 2

Let \(K = \mathbb {Q}[\sqrt {2},\sqrt {3},\sqrt {5}]\). Show that \(K\) is Galois over \(\mathbb {Q}\) and identify \(\operatorname {Gal}(K/\mathbb {Q})\) up to isomorphism.

Raw LaTeX

Let \(K = \mathbb{Q}[\sqrt{2},\sqrt{3},\sqrt{5}]\). Show that \(K\) is Galois
over \(\mathbb{Q}\) and identify \(\operatorname{Gal}(K/\mathbb{Q})\) up to
isomorphism.

Topic Tags

Galois Theory