Geodesic
Galois Groups of Even Sextic Polynomials
Canadian mathematical bulletin, Tome 63 (2020) no. 3, pp. 670-676

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DOI

Let $f(x)=x^{6}+ax^{4}+bx^{2}+c$ be an irreducible sextic polynomial with coefficients from a field $F$ of characteristic $\neq 2$, and let $g(x)=x^{3}+ax^{2}+bx+c$. We show how to identify the conjugacy class in $S_{6}$ of the Galois group of $f$ over $F$ using only the discriminants of $f$ and $g$ and the reducibility of a related sextic polynomial. We demonstrate that our method is useful for producing one-parameter families of even sextic polynomials with a specified Galois group.
DOI : 10.4153/S0008439519000754
Mots-clés : even polynomials, sextic, Galois group 
Awtrey, Chad; Jakes, Peter. Galois Groups of Even Sextic Polynomials. Canadian mathematical bulletin, Tome 63 (2020) no. 3, pp. 670-676. doi: 10.4153/S0008439519000754
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     title = {Galois {Groups} of {Even} {Sextic} {Polynomials}},
     journal = {Canadian mathematical bulletin},
     pages = {670--676},
     year = {2020},
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     number = {3},
     doi = {10.4153/S0008439519000754},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000754/}
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