Advertisement

Journal of Mathematical Sciences

, Volume 136, Issue 3, pp 3984–3987 | Cite as

On Galois spectra of polynomials with integral parameters

  • A. E. Sergeev
  • A. V. Yakovlev
Article

Abstract

We prove that there exists a polynomial F(x, t) with rational coefficients, whose degree with respect to x is equal to 4, such that for every integer a, the Galois group of the decomposition field of the polynomial F(x, a) is not the dihedral group, but any other transitive subgroup of the group S4 can be represented as the Galois group of the decomposition field of the polynomial F(x, a) for a certain integer a. Bibliography: 1 title.

Keywords

Rational Coefficient Galois Group Dihedral Group Integral Parameter Transitive Subgroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. E. Sergeev, “The inverse problem for the spectra of polynomials,” Deposited VINITI, 881-2004, 1–35 (25.05.2004).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • A. E. Sergeev
    • 1
  • A. V. Yakovlev
    • 1
  1. 1.St.Petersburg State UniversitySt.PetersburgRussia

Personalised recommendations