Let K be a nonic number field generated by a root \(\theta \) of an irreducible trinomial \( F(x)= x^9+ax+b \in {{\mathbb {Z}}}[x]\) . Let i(K) be the index of K. A prime p dividing i(K) is called a prime common index divisor of K. In this paper, for every prime p, we give necessary and sufficient conditions on a and b, so that p is a common index divisor of K. As an application of our results, we identify new infinite parametric families of non-monogenic nonic numbers fields defined by such trinomials. Our method based on a theorem of Ore (Math Ann 99:84–117, 1928) on decomposition of primes in number fields and Newton polygons of higher order as introduced by Guàrdia et al. (Trans Am Math Soc 364:361–416, 2012). At the end, some numerical examples illustrating our theoretical results are given.
