Let f (x) =x⁶+Ax³+B Zx, with A 0, and suppose that f (x) is irreducible over Q. We define f (x) to be monogenic if \1, θ, θ², θ³, θ⁴, θ^{5\} is a basis for the ring of integers of Q (θ), where f (θ) =0. For each possible Galois group G of f (x) over Q, we use a theorem of Jakhar, Khanduja and Sangwan to give explicit descriptions of all monogenic trinomials f (x) having Galois group G. We also investigate when these trinomials generate distinct sextic fields.
Harrington et al. (Tue,) studied this question.
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