On the construction of pure number fields of odd degrees with large 2-class groups
Let \(n\) be an odd integer \(>1\) and let \(\Delta_ n\) denote the number of positive divisors of \(n\) smaller than \(n\). In a previous paper [Arch. Math. 42, 53-57 (1984; Zbl 0531.12006)] the author constructed infinitely many pure number fields of degree \(n\) whose ideal class groups have 2-rank at least \(2\Delta_ n\). In the present paper he proves a stronger result where \(2\Delta_ n\) is replaced by \(3\Delta_ n\).
scientific article; zbMATH DE number 3950655