A note on l-class groups of certain algebraic number fields

Abstract

The structure of ideal class groups of number fields is investigated in the following three cases: (i) Abelian extensions of number fields whose Galois groups are of type ( p, p); (ii) non-Galois extensions Q(p d 0 3 ,p d 1 3 ) of degree p 2 over Q; (iii) dihedral extensions of degree 2 n + 1 over Q. It is shown that it is possible to obtain class number relations by group-theoretic methods. Subgroups of ideal class groups whose orders are prime to the extension degree are considered.