Imaginary Bicyclic Biquadratic Fields With Cyclic 2-Class Group
نویسندگان
چکیده
منابع مشابه
Quadratic Fields with Cyclic 2-class Groups
For any integer k ≥ 1, we show that there are infinitely many complex quadratic fields whose 2-class groups are cyclic of order 2. The proof combines the circle method with an algebraic criterion for a complex quadratic ideal class to be a square. In memory of David Hayes.
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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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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1995
ISSN: 0022-314X
DOI: 10.1006/jnth.1995.1079