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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 1996 • Question 9

Question

Math 6310 • Algebra Fall 1996 • Question 9

Let \(K\) be a field of characteristic zero. Let \(L\) be the splitting field of the polynomial \(X^n-a\) for some \(a\in K\) and some integer \(n\ge 1\). Show that the Galois group of \(L\) over \(K\) is solvable.

Raw LaTeX

Let \(K\) be a field of characteristic zero. Let \(L\) be the splitting field of the polynomial
\(X^n-a\) for some \(a\in K\) and some integer \(n\ge 1\). Show that the Galois group of \(L\) over \(K\)
is solvable.

Topic Tags

Galois Groups of Polynomials Galois Theory Solvable Groups Splitting Fields