### Imaginary Quadratic Fields k with Cl_{2}(k) = (2,2^{m}) and Rank Cl_{2}(k^{1}) = 2, by E. Benjamin, F. Lemmermeyer, and C. Snyder

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.

E. Benjamin <benjamin@mint.net>
F. Lemmermeyer <hb3@ix.urz.uni-heidelberg.de>
C. Snyder <snyder@gauss.umemat.maine.edu>