On common index divisor and monogenity of certain number fields defined by trinomials X ⁶ + AX + B

Abstract

For a number field K defined by a trinomial F (x) = x ⁶ + ax + b ∈ ℤ[x], Jakhar and Kumar gave some necessary conditions on a and b, which guarantee the non-monogenity of K [25]. In this paper, for every prime integer p, we characterize when p is a common index divisor of K. In particular, if any one of these conditions holds, then K is not monogenic. In such a way our proposed results extend those of Jakhar and Kumar.