The 2-Class Group of Certain Families of Imaginary Triquadratic Fields

Our goal in this paper is to compute the 2-rank of the class group of the fields K = Q(v-2, vq,vd) for any odd positive squarefree integer d and any prime integer q = 5 (mod 8). Furthermore, we give the list of these fields whose 2-class groups are trivial, cyclic, of type (2, 2), (2,4) or (2,2, 2).