Abstract
In this paper we give a large number of quadratic fields Q ( d ) {\mathbf {Q}}(\sqrt d ) whose class group H ( d ) H(d) has 3-Sylow subgroup H 3 ( d ) {H_3}(d) with rank r 3 ( d ) > 1 {r_3}(d) > 1 . They include 20 discriminants d > 0 d > 0 with r 3 ( d ) = 5 {r_3}(d) = 5 . The associate real fields have r 3 ( d ′ ) = 4 {r_3}(d’ ) = 4 . The distribution of the H 3 ( d ) {H_3}(d) is studied and its relative frequency is compared with the heuristic conjectures of Cohen and Lenstra. Some of the H ( d ) H(d) are recorded since they are of special interest. Some related topics are also considered.
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