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Structure of l-class groups of certain number fields and ℤl-extensions
Published online by Cambridge University Press: 26 February 2010
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Let l be a rational prime, and let ℤl denote the ring of l-adic integers. Let k0 be a finite extension field of the rational numbers ℚ, and let K be a ℤl-extension of k0 (i.e., Gal (K/k0) is topologically isomorphic to the additive group of Zl). Let the intermediate fields be denoted as follows:
where knk0 is a cyclic extension of degree ln, and Let An denote the l-class group of kn (i.e., the Sylow l-subgroup of the ideal class group of kn). It is known that the order of An is given by , with
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