On 2-class field towers of imaginary quadratic number fields

By the results of Golod-Shafarevich and Vinberg-Gaschutz, the 2-class field tower of an imaginary quadratic number field K is infinite if the 2-rank of the ideal class group of K is greater than or equal to 5. In our earlier paper, we examined the case where the 2-class rank of K is equal to 4, and proved that the 2-class åeld tower of K is infinite if K has only one negative prime discriminant, except for one type of Redei matrix of K. In this paper, we investigate the case where all the prime discriminants of K are negative, by classifying the Redei matrices of K