New number fields with known p-class tower
نویسندگان
چکیده
منابع مشابه
p-Capitulation over Number Fields with p-Class Rank Two
Theoretical foundations of a new algorithm for determining the p-capitulation type K ( ) of a number field K with p-class rank = 2 are presented. Since K ( ) alone is insufficient for identifying the second p-class group p K K = 2 Gal(F | ) G of K, complementary techniques are developed for finding the nilpotency class and coclass of G . An implementation of the complete algorithm in the ...
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The modern theory of class field towers has its origins in the study of the p-class field tower over a quadratic imaginary number field, so it is fitting that this problem be the first in the discipline to be nearing a solution. We survey the state of the subject and present a new cohomological condition for a quadratic imaginary number field to have an infinite p-class field tower (for p odd)....
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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...
متن کاملNumber fields with large class groups
After a review of the quadratic case, a general problem about the existence of number fields of a fixed degree with extremely large class numbers is formulated. This problem is solved for abelian cubic fields. Then some conditional results proven elsewhere are discussed about totally real number fields of a fixed degree, each of whose normal closure has the symmetric group as Galois group.
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ژورنال
عنوان ژورنال: Tatra Mountains Mathematical Publications
سال: 2015
ISSN: 1210-3195
DOI: 10.1515/tmmp-2015-0040