Let f(x)=x¹²+ax⁶+b ∈ Z[x], with ab nonzero. We say that f(x) is monogenic if f(x) is irreducible over Q and {1,θ,θ²,...,θ¹¹} 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 give explicit descriptions of all monogenic trinomials f(x) having Galois group G. These results extend recent work on monogenic power-compositional quartic and sextic trinomials.

The author thanks the anonymous referee for a careful reading of this article, and for all the excellent suggestions.