ON THE CLASS FIELD TOWER OF AN IMAGINARY QUADRATIC NUMBER FIELD
نویسندگان
چکیده
منابع مشابه
On 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.
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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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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...
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We construct an infinite family of imaginary quadratic number fields with 2-class groups of type (2, 2, 2) whose Hilbert 2-class fields are finite.
متن کاملL - Functions and Class Numbers of Imaginary Quadratic Fields and of Quadratic Extensions of an Imaginary Quadratic Field
Starting from the analytic class number formula involving its Lfunction, we first give an expression for the class number of an imaginary quadratic field which, in the case of large discriminants, provides us with a much more powerful numerical technique than that of counting the number of reduced definite positive binary quadratic forms, as has been used by Buell in order to compute his class ...
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ژورنال
عنوان ژورنال: Memoirs of the Faculty of Science, Kyushu University. Series A, Mathematics
سال: 1977
ISSN: 0373-6385
DOI: 10.2206/kyushumfs.31.165