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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6320 • Algebra II

Fall 2025 • Question 3

Question

Math 6320 • Algebra II Fall 2025 • Question 3

Let \(\zeta _8 = \exp (2\pi i/8)\), complex eight root of one. Use Galois theory to determine all subfields of \(\mathbb {Q}(\zeta _8)\).

Raw LaTeX

Let \(\zeta_8 = \exp(2\pi i/8)\), complex eight root of one. Use Galois
theory to determine all subfields of \(\mathbb{Q}(\zeta_8)\).

Topic Tags

Cyclotomic Fields Galois Theory