On the 2-Component of the Group of Classes of Certain Cyclic Extensions of Degree 2N Original Research Article

We give a necessary and sufficient condition for the 2-class group of a cyclic extension K/image of C.M. type and of degree 2n (n ≥ 2) to be cyclic. We also determine the exponent of the 2-class group in this case. This result is quite different from those obtained for the imaginary quadratic fields.