Imaginary Quadratic Fields k with Cl<sub>2</sub>(k) = (2,2<sup>m</sup>) and Rank Cl<sub>2</sub>(k<sup>1</sup>) = 2

Imaginary Quadratic Fields k with Cl₂(k) = (2,2^m) 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 (2,2^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.

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E. Benjamin <benjamin@mint.net>

F. Lemmermeyer <hb3@ix.urz.uni-heidelberg.de>

C. Snyder <snyder@gauss.umemat.maine.edu>