A complete characterization of indices of nonic number fields defined by x 9 + ax 2 + b

The main goal of this paper is to calculate the index of any nonic number field [Formula: see text] generated by a root [Formula: see text] of a monic irreducible trinomial [Formula: see text]. Namely, for every rational prime [Formula: see text], we calculate [Formula: see text]. As an application of our results, if [Formula: see text], then [Formula: see text] is not monogenic. We illustrate our results by some computational examples.