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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 1998 • Question 3

Question

Math 6310 • Algebra Fall 1998 • Question 3

Let \(k\) be a field containing a primitive \(n^{\mathrm {th}}\) root of unity. Show that for any \(a\in k\) the Galois group of \(X^n-a\) over \(k\) is abelian.

Raw LaTeX

Let \(k\) be a field containing a primitive \(n^{\mathrm{th}}\) root of unity. Show that for any
\(a\in k\) the Galois group of \(X^n-a\) over \(k\) is abelian.

Topic Tags

Abelian Groups and Classification of Finite Abelian Groups Cyclotomic Fields Galois Theory