Minnesota Journal of Undergraduate Mathematics

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

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Abstract

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.