Quadratic function fields with invariant class group
نویسندگان
چکیده
منابع مشابه
The 4-class Group of Real Quadratic Number Fields
In this paper we give an elementary proof of results on the structure of 4-class groups of real quadratic number fields originally due to A. Scholz. In a second (and independent) section we strengthen C. Maire’s result that the 2-class field tower of a real quadratic number field is infinite if its ideal class group has 4-rank ≥ 4, using a technique due to F. Hajir.
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The author has computed the class groups of all complex quadratic number fields Q(\f^~D) °f discriminant D for 0 < D < 4000000. In so doing, it was found that the first occurrences of rank three in the 3-Sylow subgroup are D = 3321607 = prime, class group C(3) x C(3) x C(9.7) (C(n) a cyclic group of order n), and D = 3640387 = 421.8647, class group C(3) X C(3) X C(9.2). The author has also foun...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1977
ISSN: 0022-314X
DOI: 10.1016/0022-314x(77)90026-9