Show that if the field \(F\) contains a primitive \(n^{\mathrm {th}}\)-root of unity, then the Galois group of the polynomial \(x^n-a\in F[x]\), \(a\in F\), is abelian.
Question
Math 6310 • Algebra
Fall 1994 • Question 5
Question
Fall 1994 • Question 5
Show that if the field \(F\) contains a primitive \(n^{\mathrm {th}}\)-root of unity, then the Galois group of the polynomial \(x^n-a\in F[x]\), \(a\in F\), is abelian.