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

Llorente, Pascual; Quer, Jordi

doi:10.1090/S0025-5718-1988-0917838-7

On the $3$-Sylow subgroup of the class group of quadratic fields
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by Pascual Llorente and Jordi Quer PDF

Math. Comp. 50 (1988), 321-333 Request permission

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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