Refined lower bounds on the 2-class number of the Hilbert 2-class field of imaginary quadratic number fields with elementary 2-class group of rank 3

Let k be an imaginary quadratic number field with C-k,C- 2, the 2-Sylow subgroup of its ideal class group, isomorphic to Z/2Z x Z/2Z x Z/2Z. By the use of various versions of the Kuroda das number formula, we improve significantly upon our previous lower bound for \Ck(1), 2\ the 2-class number of the Hilbert 2-class field of k. (C) 1999 Academic Press.