where En+ is the group of units in F,+ and To is the subgroup of circular units in E.+.' Let Gn denote the Galois group of Fn over Q and let 9R = Z[Gn] be the group ring of Gn over the ring of rational integers Z. In the present paper, we shall first transform the formula (1) and show that the first factor halso can be expressed as a group index of certain additive groups in R. In general, any such class number formula suggests the existence of deeper group-theoretical relations between the ideal class group and the factor group by the order of which the class number is expressed.2 In the rest of the paper, we shall study such relations between the two groups involved in our formula for he-.
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Kenkichi Iwasawa (1962) studied this question.