2-Class groups of cyclotomic towers of imaginary biquadratic fields and applications

摘要

Let d be an odd positive square-free integer. In this paper, we shall investigate the structure of the 2-class group of the cyclotomic Z(2)-extension of the imaginary biquadratic number field Q(root d, root-1) if d is of specifiic form. Furthermore, we deduce the structure of the 2-class group of the cyclotomic Z(2)-extension of Q(root-d).