On characterization of prime divisors of the index of a quadrinomial

Let θ be an algebraic integer and f(x)=xⁿ+axⁿ⁻¹+bx+c be the minimal polynomial of θ over the rationals. Let K=Q(θ) be a number field and OK be the ring of integers of $K.$ In this article, we characterize all the prime divisors of the discriminant of $f(x)$ which do not divide the index of $f(x).$ As a fascinating corollary, we deduce necessary and sufficient conditions for the monogenity of the field K=Q(θ), where θ is associated with certain quadrinomials.