Focusing on a particular case, we will show that one can explicitly determine the quartic fields \(\mathbf{K}\) that have ideal class groups of exponent \(\leqslant 2\), provided that \(\mathbf{K} / \mathbf{Q}\) is not normal, provided that \(\mathbf{K}\) is a quadratic extension of a fixed imaginar
โฆ LIBER โฆ
Abelian 2-class field towers over the cyclotomic({mathbb {Z}_2})-extensions of imaginary quadratic fields
โ Scribed by Yasushi Mizusawa; Manabu Ozaki
- Publisher
- Springer
- Year
- 2009
- Tongue
- English
- Weight
- 267 KB
- Volume
- 347
- Category
- Article
- ISSN
- 0025-5831
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
The Exponent 2-Class-Group Problem for N
โ
S. Louboutin
๐
Article
๐
1994
๐
Elsevier Science
๐
English
โ 350 KB
On the Galois groups of the 2-class towe
โ
Aliza Steurer
๐
Article
๐
2007
๐
Elsevier Science
๐
English
โ 165 KB
Denominators of Eisenstein cohomology cl
โ
Tobias Berger
๐
Article
๐
2007
๐
Springer
๐
English
โ 482 KB
On the 2-part of the class number of ima
โ
Arnold Pizer
๐
Article
๐
1976
๐
Elsevier Science
๐
English
โ 363 KB
On the maximal unramified pro-2-extensio
โ
Yasushi Mizusawa
๐
Article
๐
2004
๐
Elsevier Science
๐
English
โ 230 KB
In this paper, we construct an infinite family of real quadratic fields k such that the maximal unramified pro-2-extension of the cyclotomic Z 2 -extension of k is a finite non-abelian extension.
Refined Lower Bounds on the 2-Class Numb
โ
Elliot Benjamin; Charles J. Parry
๐
Article
๐
1999
๐
Elsevier Science
๐
English
โ 125 KB
Let k be an imaginary quadratic number field with C k, 2 , the 2-Sylow subgroup of its ideal class group, isomorphic to Zร2Z\_Zร2Z\_Zร2Z. By the use of various versions of the Kuroda class number formula, we improve significantly upon our previous lower bound for |C k 1 , 2 | , the 2-class number of