On the l-part of the Class Groups of Imaginary Cyclic Fields of Conductor p and Degree 2ln

Let l be a fixed odd prime number, and p = 2qle + 1 an odd prime number with (q, 2l) = 1. For 0 ≤ n ≤ e, let kn be the subfield of the pth cyclotomic field Q(ζp) of degree 2ln. It is an imaginary cyclic field of conductor p. We study the Galois module structure and Iwasawa type “class number formula” of the l-part of the class groups of kn. Moreover, we give numerical examples for p < 1, 000, 000.