Geodesic
Computing Galois groups of certain families of polynomials
Khosro Monsef Shokri1 ; Jafar Shaffaf1 ; Reza Taleb1
1 Department of Mathematical Sciences Shahid Beheshti University P.O. Box 19839-63113, Tehran, Iran
Acta Arithmetica, Tome 185 (2018) no. 4, pp. 357-365.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

There are several results on computing the Galois groups of different families of trinomials with integer coefficients. However, adding even one more term to a trinomial makes this computation very complicated due to some problems including the complexity of finding a formula for the discriminant. We show that the Galois group of certain irreducible quadrinomials of the form $f(x)=x^{n}+ax^{n-1}+bx^{n-2}+c\in \mathbb{Z}[x]$ is the full symmetric group $S_n$, and furthermore we generalize the results to a certain family of polynomials with an arbitrary number of terms.
DOI : 10.4064/aa171014-26-2
Keywords: there several results computing galois groups different families trinomials integer coefficients however adding even term trinomial makes computation complicated due problems including complexity finding formula discriminant galois group certain irreducible quadrinomials form n n mathbb full symmetric group nbsp furthermore generalize results certain family polynomials arbitrary number terms

Khosro Monsef Shokri 1 ; Jafar Shaffaf 1 ; Reza Taleb 1

1 Department of Mathematical Sciences Shahid Beheshti University P.O. Box 19839-63113, Tehran, Iran 
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Khosro Monsef Shokri; Jafar Shaffaf; Reza Taleb. Computing Galois groups of certain families of polynomials. Acta Arithmetica, Tome 185 (2018) no. 4, pp. 357-365. doi : 10.4064/aa171014-26-2. http://geodesic.mathdoc.fr/articles/10.4064/aa171014-26-2/

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