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 511For any octic number field $K$ generated by a root $α$ of a monic irreducible trinomial $F(x)=x^8+ax^3+b \in \mathbb{Z}[x]$ 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.