On Galois spectra of polynomials with integral parameters
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.
KeywordsRational Coefficient Galois Group Dihedral Group Integral Parameter Transitive Subgroup
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- 1.A. E. Sergeev, “The inverse problem for the spectra of polynomials,” Deposited VINITI, 881-2004, 1–35 (25.05.2004).Google Scholar