Elliot Benjamin, Franz Lemmermeyer, Chip Snyder
Published 2000-03-27Version 1
We classify all complex quadratic number fields with 2-class group of type (2,2^m) whose Hilbert 2-class fields have class groups of 2-rank equal to 2. These fields all have 2-class field tower of length 2. We still don't know examples of fields with 2-class field tower of length 3, but the smallest candidate is the field with discriminant -1015.
On the exponents of class groups of some families of imaginary quadratic fields
Imaginary quadratic fields with Cl_2(k) = (2,2,2)
$2^\infty$-Selmer groups, $2^\infty$-class groups, and Goldfeld's conjecture
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