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On nilpotent factors of congruent ideal class groups of Galois extensions

Published online by Cambridge University Press:  22 January 2016

Yoshiomi Furuta
Yoshiomi Furuta*
Affiliation:
Kanazawa University
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Let K be a Galois extension of an algebraic number field k of finite degree with Galois group g. Then g acts on a congruent ideal class group of K as a group of automorphisms, when the class field M over K corresponding to is normal over K. Let Ig be the augmentation ideal of the group ring Zg over the ring of integers Z, namely Ig be the ideal of Zg generated by σ − 1, σ running over all elements of g. Then is the group of all elements aσ-1 where a and σ belong to and g respectively.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 62 , September 1976 , pp. 13 - 28
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1976

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