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Special units and ideal class groups of extensions of imaginary quadratic fields

Published online by Cambridge University Press:  01 September 2007

BYUNGCHUL CHA
BYUNGCHUL CHA*
Affiliation:
Department of Mathematics and Computer Science, Hendrix College Conway, AR 72032, U.S.A. email: cha@hendrix.edu
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Extract

Let K be an imaginary quadratic field, and let F be an abelian extension of K, containing the Hilbert class field of K. We fix a rational prime p > 2 which does not divide the number of roots of unity in the Hilbert class field of K. Also, we assume that the prime p does not divide the order of the Galois group G:=Gal(F/K). Let AF be the ideal class group of F, and EF be the group of global units of F. The purpose of this paper is to study the Galois module structures of AF and EF.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 143 , Issue 2 , September 2007 , pp. 265 - 270
Copyright
Copyright © Cambridge Philosophical Society 2007

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References

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