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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



On the $ 3$-Sylow subgroup of the class group of quadratic fields

Authors: Pascual Llorente and Jordi Quer
Journal: Math. Comp. 50 (1988), 321-333
MSC: Primary 11R11; Secondary 11R29
MathSciNet review: 917838
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Abstract: In this paper we give a large number of quadratic fields $ {\mathbf{Q}}(\sqrt d )$ whose class group $ H(d)$ has 3-Sylow subgroup $ {H_3}(d)$ with rank $ {r_3}(d) > 1$. They include 20 discriminants $ d < 0$ with $ {r_3}(d) = 5$. The associate real fields have $ {r_3}(d' ) = 4$. The distribution of the $ {H_3}(d)$ is studied and its relative frequency is compared with the heuristic conjectures of Cohen and Lenstra. Some of the $ H(d)$ are recorded since they are of special interest. Some related topics are also considered.

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Keywords: Quadratic fields, class group
Article copyright: © Copyright 1988 American Mathematical Society

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