Number fields with class number congruent to 4 mod 8 and Hilbert's theorem 94

Der Briefwechsel Hasse - Scholz - Taussky

“…Der folgende Satz enthält Teilresultate von Furtwängler [86], Kisilevsky [152], sowie Couture & Derhem [59]:…”

On the maximal unramified pro-2-extension of Z2-extensions of certain real quadratic fields II

“…As mentioned in the Introduction, under the assumption that Greenberg's conjecture holds, it seems that the Galois group G = Gal(L(k ∞ )/k ∞ ) for totally real k ∞ has similar properties to the Galois group of a 2-class field tower of a finite extension of Q. By the results of Kisilevsky [10] and Benjamin-Snyder [5], all the types Q 2 m , D 2 m , SD 2 m , (2, 2) appear as the Galois groups of 2-class field towers of quadratic fields. From this point of view, we have the following question.…”

“…By the theorem of H. Kisilevsky [10], we can characterize the structure of the Galois group G = Gal(L(k)/k) by the order of the kernel of j and the Taussky conditions as in Table 2. Table 2 (by the theorem in [10], m ≥ 3)…”

Sur la tour de Hilbert de certains corps

“…D'après [3] et [8], on a que si C k,2 est un groupe élémentaire de rang 2, alors C k 1 ,2 est cyclique, ce qui donne que la tour des 2-corps de classes de Hilbert s'arrête en k 1 ou en k 2 .…”