Irreducible sextic polynomials and their absolute resolvents

  • Chad Awtrey Elon University
  • Robin French Williams High School, Burlington, NC
  • Peter Jakes Elon University
  • Alan Russell Elon University


We describe two new algorithms for determining the Galois group of an irreducible polynomial of degree six defined over the rational numbers.  Both approaches are based on the absolute resolvent method, which involves analyzing polynomials defining subfields of the original polynomial's splitting field.  Compared to the traditional algorithm for degree six Galois groups due to Cohen, our methods can be considered improvements since one uses fewer resolvents and the other uses lower degree resolvents.
How to Cite
AWTREY, Chad et al. Irreducible sextic polynomials and their absolute resolvents. Minnesota Journal of Undergraduate Mathematics, [S.l.], v. 1, n. 1, dec. 2015. ISSN 2378-5810. Available at: <>. Date accessed: 19 feb. 2020.