On monogenity of certain pure number fields of degrees $2^r\cdot3^k\cdot7^s$

Let $K = \mathbb{Q} (\alpha) $ be a pure number field generated by a complex root $\alpha$ of a monic irreducible polynomial $ F(x) = x^{2^r\cdot3^k\cdot7^s} -m \in\bb{Z}[x]$, where $r$, $k$, $s$ are three positive natural integers. The purpose of this paper is to study the monogenity of $K$. Our results are illustrated by some examples.