On 2-class field towers of imaginary quadratic number fields

By the results of Golod-Shafarevich and Vinberg-Gaschutz, the 2-classfield tower of an imaginary quadratic number field K is infinite if the 2-rankof the ideal class group of K is greater than or equal to 5. In our earlierpaper, we examined the case where the 2-class rank of K is equal to 4, andproved that the 2-class åeld tower of K is infinite if K has only one negativeprime 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