Article

Subfields of Solvable Sextic Field Extensions

---

Abstract

Let F be a field, f(x) in F[x] an irreducible polynomial of degree six, K the stem field of f, and G the Galois group of f over F. We show G is solvable if and only if K/F has either a quadratic or cubic subfield. We also show that G can be determined by: the size of the automorphism group of K/F, the discriminant of f, and the discriminants of polynomials defining intermediate fields. Since most methods for computing polynomials defining intermediate subfields require factoring f over its stem, we include a method that does not require factorization over K, but rather only relies factoring two linear resolvent polynomials over F.

Keywords: sextic polynomials, Galois group computation, subfields, linear resolvents

How to Cite:

Awtrey, C. & Jakes, P., (2018) “Subfields of Solvable Sextic Field Extensions”, North Carolina Journal of Mathematics and Statistics 4(1).