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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Densities for ranks of certain parts of $ p$-class groups


Author: Frank Gerth
Journal: Proc. Amer. Math. Soc. 99 (1987), 1-8
MSC: Primary 11R18; Secondary 11R29
MathSciNet review: 866419
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Abstract: Let $ K$ be a Galois extension of the field of rational numbers of prime degree $ p$, and let $ {C_K}$ be the $ p$-class group of $ K$. In this paper densities for the ranks of certain parts of such $ {C_K}$ are calculated, and these densities suggest a way to extend conjectures of Cohen and Lenstra.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0866419-3
PII: S 0002-9939(1987)0866419-3
Article copyright: © Copyright 1987 American Mathematical Society