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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Kida's theorem for a class of nonnormal extensions


Authors: Robert Gold and Manohar Madan
Journal: Proc. Amer. Math. Soc. 104 (1988), 55-60
MSC: Primary 11R23
DOI: https://doi.org/10.1090/S0002-9939-1988-0958043-X
MathSciNet review: 958043
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Abstract: Let $ E,F$ be $ {{\mathbf{Z}}_p}$-fields of CM-type such that $ E/F$ is an extension of degree $ p$. Let $ L$, the normal closure of $ E/F$, be such that $ \operatorname{Gal} (L/F)$ has a normal subgroup of order $ p$. Denote the fixed field of this group by $ K$. We prove a Kida type formula which describes the minus part of the Iwasawa lambda invariant of $ E$ in terms of the lambda invariants of $ F$ and $ K$.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0958043-X
Article copyright: © Copyright 1988 American Mathematical Society