Imaginary Quadratic Fields k with Cl2(k) = (2,2m) and Rank Cl2(k1) = 2, by E. Benjamin, F. Lemmermeyer, and C. Snyder

We classify all complex quadratic number fields with 2-class group of type (2,2m) 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.

E. Benjamin <>
F. Lemmermeyer <>
C. Snyder <>