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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6320 • Algebra II

Fall 2023 • Question 5

Question

Math 6320 • Algebra II Fall 2023 • Question 5

Find the Galois group of \(x^8-2 \in \mathbb {Q}[x]\). In particular, prove that it has order 16 and is not the dihedral group.

Raw LaTeX

Find the Galois group of \(x^8-2 \in \mathbb{Q}[x]\). In particular, prove
that it has order 16 and is not the dihedral group.

Topic Tags

Galois Groups of Polynomials Galois Theory