Geodesic
On the Galois spectra of polynomials with integral parameters
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 12, Tome 321 (2005), pp. 275-280

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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 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 $S_4$ can be represented as the Galois group of the decomposition field of the polynomial $F(x,a)$ for some integer $a$. 
@article{ZNSL_2005_321_a15,
     author = {A. \`E. Sergeev and A. V. Yakovlev},
     title = {On the {Galois} spectra of polynomials with integral parameters},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {275--280},
     publisher = {mathdoc},
     volume = {321},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_321_a15/}
}
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A. È. Sergeev; A. V. Yakovlev. On the Galois spectra of polynomials with integral parameters. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 12, Tome 321 (2005), pp. 275-280. http://geodesic.mathdoc.fr/item/ZNSL_2005_321_a15/