Relative Integral Bases of Number Fields of Type (q~s,q~s,…,q~s)

Let K be an abelian number field, and let Kbe its genus field. A simple construction of Kwas given in Ref. [1]. We here give a further description of K, which determines the conductor f(K) and discriminant D(K). And, using these results. we prove that an extension L/K of type (q~s, q~s,…, q~s) has a relative integral basis under some conditions. Suppose that L is any algebraic number field containing K as a subfield. Since the