Imaginary Quadratic Fields k with Cyclic Cl_2(k^1), by Elliot Benjamin, Franz Lemmermeyer, Chip Snyder

This paper has appeared in J. Number Theory 67 (1997), no. 2, 229-245, and so the dvi version has been removed. Let $k$ be an imaginary quadratic number field, and let $k^1$ denote its Hilbert $2$-class field. In this paper, we determine the fields $k$ such that the $2$-class group of $k^1$ is cyclic. In particular, such fields have terminating $2$-class field tower.

Elliot Benjamin, Franz Lemmermeyer, Chip Snyder <lemmermf@cs.uni-sb.de, snyder@gauss.umemat.maine.edu>