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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On the ideal class group of real biquadratic fields


Author: Patrick J. Sime
Journal: Trans. Amer. Math. Soc. 347 (1995), 4855-4876
MSC: Primary 11R29; Secondary 11R16
DOI: https://doi.org/10.1090/S0002-9947-1995-1333398-3
MathSciNet review: 1333398
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Abstract: We discuss the structure of the ideal class group of real biquadratic fields $ K$, concentrating on the case that the $ 4$-rank of the ideal class groups of the quadratic subfields of $ K$ is 0. In this case, we give estimates for the $ 4$-rank of the ideal class group of $ K$. As an example, let $ K = \mathbb{Q}(\sqrt p ,\sqrt {627} )$, where $ p$ is a prime satisfying certain congruence conditions. The $ 2$-primary part of the ideal class group of $ K$ is then isomorphic to $ {(\mathbb{Z}/4\mathbb{Z})^2},\mathbb{Z}/4\mathbb{Z} \times {(\mathbb{Z}/2\mathbb{Z})^2}$, or $ {(\mathbb{Z}/2\mathbb{Z})^4}$. Further, each of the above occurs infinitely often.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1995-1333398-3
Article copyright: © Copyright 1995 American Mathematical Society

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