Dihedral Galois groups of even degree polynomials

Maria Ángeles Gómez-Molleda

Vol. 229 (2007), No. 1, 185–197

DOI: 10.2140/pjm.2007.229.185

Abstract

We present a new characterization of dihedral Galois groups of rational irreducible polynomials. It allows us to reduce the problem of deciding whether the Galois group of an even degree polynomial is dihedral, and its computation in the affirmative case, to the case of a quartic or odd degree polynomial, for which algorithms already exist. The characterization and algorithm are extended to permutation groups of order 2n containing an n-cycle.

Keywords

Dihedral Galois group, polynomials

Mathematical Subject Classification 2000

Primary: 12Y05

Secondary: 11R32

Milestones

Received: 17 May 2005

Accepted: 11 January 2006

Published: 1 January 2007