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The ambiguous class group and the genius group of certain non-normal extensions

Published online by Cambridge University Press:  26 February 2010

Colin D. Walter
Colin D. Walter
Affiliation:
Department of Mathematics, University College, Belfield, Dublin 4, Ireland
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Extract

In an article generalising work of Roquette and Zassenhaus, Connell and Sussman [2] have demonstrated the importance of certain prime ideals in a number field k0 for estimating the l-rank of the class group of an extension k. These ideals have a power prime to l which is principal and all their prime factors in k have ramification index divisible by l. The products of the prime divisors of these ideals in the normal closure K of k/k0 are invariant under Gal (k/k0). Thus certain roots in k of the ideals in k0 are in some sense fixed by the Galois group. This leads to the concept of ambiguous ideals in an extension k/k0 which is not necessarily normal.

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Type
Research Article
Information
Mathematika , Volume 26 , Issue 1 , June 1979, pp. 113 - 124
Copyright
Copyright © University College London 1979

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