Power integral bases for certain pure sextic fields

In this paper, we characterize whether the pure sextic fields [Formula: see text] with square-free integers m ≢ ±1( Mod 9) have power integral bases or do not; if m ≡ 2, 3 (Mod 4), then [Formula: see text] have power integral bases. We prove this by determining relative integral bases of such fields with respect to their cubic and quadratic subfields. Based on the works of Kovács and Pethő, several examples on application of monogenic fields to CNS (Canonical Number System) are shown.