Monogenic Reciprocal Quartic Polynomials And Their Galois Groups

Suppose that f(x)=x⁴+Ax³+Bx²+Ax+1∈ Z[x]. We say that $f(x)$ is monogenic if $f(x)$ is irreducible over Q and \1,θ,θ²,θ³\ is a basis for the ring of integers of Q(θ), where f(θ)=0. For each possible Galois group G that can occur in the two cases of A≠ 0 with $B=0$, and AB≠ 0, we determine all monogenic polynomials $f(x)$ with Galois group G.