Pure fields of degree 9 with class number prime to 3
نویسندگان
چکیده
منابع مشابه
On divisibility of the class number h+ of the real cyclotomic fields of prime degree l
In this paper, criteria of divisibility of the class number h+ of the real cyclotomic field Q(ζp +ζ−1 p ) of a prime conductor p and of a prime degree l by primes q the order modulo l of which is l−1 2 , are given. A corollary of these criteria is the possibility to make a computational proof that a given q does not divide h+ for any p (conductor) such that both p−1 2 , p−3 4 are primes. Note t...
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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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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 1980
ISSN: 0373-0956
DOI: 10.5802/aif.781