Infinite Hilbert 2-class field tower of quadratic number fields
نویسندگان
چکیده
منابع مشابه
On Imaginary Quadratic Number Fields with 2-class Group of Rank 4 and Infinite 2-class Field Tower
Let k be an imaginary quadratic number field with Ck,2, the 2-Sylow subgroup of its ideal class group Ck, of rank 4. We show that k has infinite 2-class field tower for particular families of fields k, according to the 4-rank of Ck, the Kronecker symbols of the primes dividing the discriminant ∆k of k, and the number of negative prime discriminants dividing ∆k. In particular we show that if the...
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We determine all real quadratic number fields with 2-class field tower of length at most 1.
متن کاملOn 2-class field towers of imaginary quadratic number fields
For a number field k, let k1 denote its Hilbert 2-class field, and put k2 = (k1)1. We will determine all imaginary quadratic number fields k such that G = Gal(k2/k) is abelian or metacyclic, and we will give G in terms of generators and relations.
متن کاملOn the 2-class Field Tower of a Quadratic Number Field
Let k = k be a quadratic number field with discriminant ∆. For n ≥ 0, we define fields k inductively by taking k as the compositum of all unramified quadratic extensions of k that are central over k. Then k(∞) = ⋃∞ n=0 k (n,2) is the 2-class field tower of k. In the following, we call k the n central 2-step. The structure of the Galois group Gal (k/k) of the first central 2-step is determined b...
متن کاملComputing the Hilbert class field of real quadratic fields
Using the units appearing in Stark’s conjectures on the values of L-functions at s = 0, we give a complete algorithm for computing an explicit generator of the Hilbert class field of a real quadratic field. Let k be a real quadratic field of discriminant dk, so that k = Q( √ dk), and let ω denote an algebraic integer such that the ring of integers of k is Ok := Z+ ωZ. An important invariant of ...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2010
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa145-3-4