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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Endô, A. On the stickelberger ideal of (2,...,2)-extensions of a cyclotomic number field. Manuscripta Math 69, 107–132 (1990). https://doi.org/10.1007/BF02567915
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DOI: https://doi.org/10.1007/BF02567915