Abstract

Let p be an odd prime number and n a natural number. Let K be a (2,...,2)-extension of the pn−th cyclotomic number field obtained by adjoining $$\sqrt {m_1 } $$ ,..., $$\sqrt {m_t } $$ , where m1,...,mt are rational integers. We get a system of generators of the minus part of the Stickelberger ideal of K, and calculate its index. This index is described as a product of some determinants of rational integer components. From this result, it is shown that the relative class number of K is expressed as this index.

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