Integral bases and monogenity of pure fields

Let m be a square-free integer (m≠0,±1). We show that the structure of the integral bases of the fields K=Q(mn) is periodic in m. For 3≤n≤9 we show that the period length is n2. We explicitly describe the integral bases, and for n=3,4,5,6,8 we explicitly calculate the index forms of K. This enables us in many cases to characterize the monogenity of these fields. Using the explicit form of the index forms yields a new technic that enables us to derive new results on monogenity and to get several former results as easy consequences. For n=4,6,8 we give an almost complete characterization of the monogenity of pure fields.