Computing Galois groups of certain families of polynomials
Acta Arithmetica, Tome 185 (2018) no. 4, pp. 357-365
Cet article a éte moissonné depuis 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.
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
Affiliations des auteurs :
Khosro Monsef Shokri 1 ; Jafar Shaffaf 1 ; Reza Taleb 1
@article{10_4064_aa171014_26_2,
author = {Khosro Monsef Shokri and Jafar Shaffaf and Reza Taleb},
title = {Computing {Galois} groups of certain families of polynomials},
journal = {Acta Arithmetica},
pages = {357--365},
year = {2018},
volume = {185},
number = {4},
doi = {10.4064/aa171014-26-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa171014-26-2/}
}
TY - JOUR AU - Khosro Monsef Shokri AU - Jafar Shaffaf AU - Reza Taleb TI - Computing Galois groups of certain families of polynomials JO - Acta Arithmetica PY - 2018 SP - 357 EP - 365 VL - 185 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4064/aa171014-26-2/ DO - 10.4064/aa171014-26-2 LA - en ID - 10_4064_aa171014_26_2 ER -
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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
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