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

On metabelian 2-class field towers over -extensions of real quadratic fields

“…The author verified it for all in the same way. A similar argument is used in the proofs of [14, Theorem 2] and [19, Theorem 3.1].…”

“…Toward this open problem, it seems a considerable problem to find various examples of fab G even in the case of metabelian G. In this paper, we focus on the case where p = 2 and k is a real quadratic field. Then there are a number of results and examples in the case of metacyclic G ( [2,14,15,16,18,19] etc.). The following main theorem gives a family of real quadratic fields k with non-metacyclic metabelian (possibly finite) G.…”

“…In this paper, we focus on the case where and k is a real quadratic field. Then there are a number of results and examples in the case of metacyclic (see [2, 14–16, 18, 19] etc.). The following main theorem gives a family of real quadratic fields k with nonmetacyclic metabelian (possibly finite) .…”

On pro-𝑝 link groups of number fields

“…There are other examples of prometacyclic G S (k cyc ) for p = 2 and quadratic k/Q (cf. [28,30,45] and Theorem 4.10). Moreover, all imaginary quadratic fields k with prometacyclic (or abelian) G ∅ (k cyc ) have been characterized (cf.…”

On the maximal unramified pro-2-extension over the cyclotomic \mathbb{Z}_2-extension of an imaginary quadratic field

“…It is conjectured that G(k ∞ ) is finitely generated as a pro-p-group, and it is true when k is an abelian extension of Q by the theorem of Ferrero-Washington [9]. Further, as a consequence of Greenberg's conjecture [14], it is conjectured that G(k ∞ ) is a FAb pro-p-group if k is a totally real number field (cf., e.g., [26]).…”