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On the central ideal class group of cyclotomic fields

Published online by Cambridge University Press:  22 January 2016

Susumu Shirai
Susumu Shirai*
Affiliation:
Toyama Medical and Pharmaceutical University
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Let Q be the rational number field, K/Q be a finite Galois extension with the Galois group G, and let CK be the ideal class group of K in the wider sense. We consider CK as a G-module. Denote by I the augmentation ideal of the group ring of G over the ring of rational integers. Then CK/I(CK) is called the central ideal class group of K, which is the maximal factor group of CK on which G acts trivially. A. Fröhlich [3, 41 rationally determined the central ideal class group of a complete Abelian field over Q whose degree is some power of a prime. The proof is based on Theorems 3 and 4 of Fröhlich [2]. D. Garbanati [6] recently gave an algorithm which will produce the l-invariants of the central ideal class group of an Abelian extension over Q for each prime l dividing its order.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 75 , September 1979 , pp. 133 - 143
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1979

References

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