Sep 12, 2012 Thread starter #1 Z zekhnini New member Sep 12, 2012 1 Let the field K=Q(sqrt{p1}, sqrt{p2q}, i) where p1, p2 are congruent to 1 mod4 and q to 3 mod4, kronecker(2,p1)=1 and kronecker(2,p2)=kronecker(p1,p2) = kronecker(p1,q)=-1. How to prove that the 2-rank of K is equal to 2.

Let the field K=Q(sqrt{p1}, sqrt{p2q}, i) where p1, p2 are congruent to 1 mod4 and q to 3 mod4, kronecker(2,p1)=1 and kronecker(2,p2)=kronecker(p1,p2) = kronecker(p1,q)=-1. How to prove that the 2-rank of K is equal to 2.