Abdelmalek Azizi, Abdelkader Zekhnini, Mohammed Taous

ON A PROBLEM OF SURRENDER THE BODY Q (root p1p2, i) WHOSE 2-GROUP OF CLASSES ARE ELEMENTARY

Let p(1) equivalent to p(2) equivalent to 1 (mod 8) be primes such that and(p(1)/p(2)) = -1 , and (2/a+b) = -1 where p (1) p (2) = a (2)+b (2). Let i = root-1,d = p (1) p (2), k= Q(root d, i), K-2((1)) be the Hilbert 2-class field and k(*) = (root p(1), root p(2), i) be the genus field of . The 2-part C-k,C-2 of the class group of is of type (2, 2, 2), so contains seven unramified quadratic extensions and seven unramified biquadratic extensions . Our goal is to determine the fourteen extensions, the group and to study the capitulation problem of the 2-classes of . the class group of k is of type ( 2, 2, 2), so k ( 1) 2 contains seven unramified quadratic extensions K j / k and seven unramified biquadratic extensions L j / k. Our goal is to determine the fourteen extensions, the group Ck, 2 and to study the capitulation problem of the 2- classes of k.
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