On index divisors and monogenity of certain octic number fields defined by x^8+ax^3+b - Kchit, Omar (Ukrains’kyi Matematychnyi Zhurnal, 2024)
UDC 511 For any octic number field K generated by a root α of a monic irreducible trinomial F(x)=x^8+ax^3+b Z[x] and for every rational prime p, we show when p divides the index of K. We also describe the prime power decomposition of the index i(K). In this way, we give a partial answer to Problem 22 of Narkiewicz [Elementary and analytic theory of algebraic numbers, Springer-Verlag, Auflage (2004)] for this family of number fields. As an application of our results, we conclude that if i(K) eq1, then K is not monogenic. We illustrate our results by some computational examples.