Malcolm Hoong Wai Chen

Elementary characterization of the Galois groups of x 12 + ax 6 + b

Abstract Let f ( x ) = x 12 + a x 6 + b ∈ Q [ x ] $f\left(x\right)={x}^{12}+a{x}^{6}+b\in \mathbb{Q}\left[x\right]$ be an irreducible polynomial, g 4 ( x ) = x 4 + ax 2 + b , g 6 ( x ) = x 6 + ax 3 + b , and let G 4 and G 6 be the Galois groups of g 4 ( x ) and g 6 ( x ), respect...