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 <email@example.com>
F. Lemmermeyer <firstname.lastname@example.org>
C. Snyder <email@example.com>