Dihedral Galois groups of even degree polynomials

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 afirmative 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.