On the class groups of pure function fields
نویسندگان
چکیده
منابع مشابه
On 3-class Groups of Certain Pure Cubic Fields
Let p be a prime number, and let K = Q( 3 √p). Let M = Q(ζ, 3 √p) = Q( √ −3, 3 √p), where ζ is a primitive cube root of unity. Let SK be the 3-class group of K (that is, the Sylow 3-subgroup of the ideal class group of K). Let SM (respectively, SQ(ζ)) be the 3-class group ofM (respectively, Q(ζ)). Since Q(ζ) has class number 1, then SQ(ζ) = {1}. Assuming p ≡ 1 (mod 9), Calegari and Emerton [3, ...
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15 صفحه اولOn the Lie Algebras Associated with Pure Mapping Class Groups
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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: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1988
ISSN: 0386-2194
DOI: 10.3792/pjaa.64.170