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Number Theory the 2-rank of a field


New member
Sep 12, 2012
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.