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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

Frank Gerth III
Frank Gerth III
Affiliation:
Department of MathematicsThe Universtity of Texas, Austin, Texas 78712, U. S. A.
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Extract

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

Type
Research Article
Information
Mathematika , Volume 24 , Issue 1 , June 1977 , pp. 16 - 33
Copyright
Copyright © University College London 1977

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References

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