On monogenity of certain pure number fields defined by $$x^{{2}^{u}.3^{v}} - m$$

Monogenity and Power Integral Bases: Recent Developments

“…A typical statement from this list is the following: Theorem 7. (L. El Fadil and A. Najim [40]) Let α be a root of the irreducible polynomial x 2 k •3 ℓ − m with a square-free m. If m ̸ ≡ 1 (mod 4) and m ̸ ≡ ±1 (mod 9) then α generates a power integral basis in K = Q(α). If m ≡ 1 (mod 4) or m ≡ 1 (mod 9), or k = 2 and m ≡ −1 (mod 9) then K is not monogenic.…”