A study of monogenity of binomial composition

Let θ be a root of a monic polynomial h(x)∈Z[x] of degree n≥2. We say that h(x) is monogenic if it is irreducible over Q and {1,θ,θ2,…,θn−1} is a basis for the ring ZK of integers of K=Q(θ). We investigate monogenity of number fields generated by roots of compositions of two binomials. We characterise all the primes dividing the index of the subgroup Z[θ] in ZK where K=Q(θ) with θ having minimal polynomial F(x)=(xm−b)n−a∈Z[x], m≥1 and n≥2. As an application, we provide a class of pairs of binomials f(x)=xn−a and g(x)=xm−b having the property that both f(x) and f(g(x)) are monogenic.