On 2-class field towers for quadratic number fields with 2-class group of type (2,2)
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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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 1998
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089500032353