Tame kernels for biquadratic number fields

Let F = Q(root- d(1)) and E = Q(root- d(1),root d(2)), d(1) and d(2) squarefree integers, be an imaginary field and a biquadratic field, respectively. Let S be the set consisting of all infinite primes, all dyadic primes and all finite primes which ramify in E. Suppose the 4-rank of the class group of F is zero and the S-ideal class group of F has odd order, we give the forms of all elements of order <= 2 in K2OE and use the Hurrelbrink and Kolster's method [ Hurrelbrink, J. and Kolster, M.: J. reine angew. Math. 499 ( 1998), 145 - 188] to obtain the forms of all elements of order 4 in K2OE.