Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4593540 | Journal of Number Theory | 2016 | 24 Pages |
Abstract
In this paper, the relations between p-ranks of the tame kernel and the ideal class group for a general number field are investigated. As a result, nearly all of Browkin's results about quadratic fields are generalized to those for general number fields. In particular, a p-rank formula between the tame kernel and the ideal class group for a totally real number field of odd degree is obtained when p is a Fermat prime. As an example, the case of cyclic quartic fields is considered in more details. More precisely, using the results on cyclic quartic fields, we give some results connecting the p-rank(K2OF)p-rank(K2OF) with the p-rank(Cl(OE))p-rank(Cl(OE)), where F is a cyclic quartic field and E is an appropriate subfield of F(ζp)F(ζp).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Chaochao Sun, Kejian Xu,