On power integral bases for certain pure number fields defined by $x^{2\cdot 3^k}-m$

On power integral bases of certain pure number fields defined by $x^{3^r\cdot 7^s}-m$

“…In [10,13,12,9,4,3,11], based on Newton polygon techniques, we studied the monogeneity of the pure number fields of degrees in the following list: 12, 18, 24, 36, p r , 3 k • 5 r , and 2 • 3 k . In this paper, based on Newton polygon techniques, we study the monogeneity of any pure number field K = Q(α) generated by a complex root of a monic irreducible polynomial F (x) = x 3 r •7 s − m, where m = ±1 is a square free integer, and r and s are positive integers.…”