The <i>l</i>-class group of the <i><b>Z</b></i><sub><i>p</i></sub>-extension over the rational field

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  • The l-class group of the Zp-extension over the rational field

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Abstract

Let p be an odd prime, and let B∞ denote the Zp-extension over the rational field. Let l be an odd prime different from p. The question whether the l-class group of B∞ is trivial has been considered in our previous papers mainly for the case where l varies with p fixed. We give a criterion, for checking the triviality of the l-class group of B∞, which enables us to discuss the triviality when p varies with l fixed. As a consequence, we find that, if l does not exceed 13 and p does not exceed 101, then the l-class group of B∞ is trivial.

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