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

Abstract

Let [Formula: see text] be an odd positive square-free integer. In this paper, we shall investigate the structure of the [Formula: see text]-class group of the cyclotomic [Formula: see text]-extension of the imaginary biquadratic number field [Formula: see text] if [Formula: see text] is of specifiic form. Furthermore, we deduce the structure of the [Formula: see text]-class group of the cyclotomic [Formula: see text]-extension of [Formula: see text].