Dihedral Galois groups of even degree polynomials

• Autores: María Angeles Gómez Molleda
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 229, Nº 1, 2007, págs. 185-198
• Idioma: inglés
• DOI: 10.2140/pjm.2007.229.185
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• Resumen

  • 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.