Imaginary quadratic fields k with Cl_2(k) = (2,2^m) and Rank Cl_2(k^1) = 2

Elliot Benjamin, Franz Lemmermeyer, Chip 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-clas…