Monogenity of the composition of certain polynomials

We call a monic irreducible polynomial f(x)∈Z[x] to be monogenic if Z[θ] is the ring of integers of the number field Q(θ) where θ is a root of f(x). Finding the ring of integers of a number field is an important problem in algebraic number theory. In this article, we establish a necessary condition for the monogenity of a composition of two polynomials. In particular, we characterise certain primes dividing the index of the composition f(xm+a) for m≥2, a∈Z, provided that f(x)∈Z[x] is a monic polynomial such that the composition f(xm+a) is irreducible. As a consequence, we are able to achieve a sufficient condition for the monogenity of f(xm+a) which in turn enables us to produce a new infinite family of monogenic polynomials.