Let G be a finite abelian group, it is a difficult and unsolved problem to find a number field F whose ideal class group is isomorphic to G. In [WAS], Corollary 3.9 and in [COR], Theorem 2, it is proved that every finite abelian group is isomorphic to a factor group of the ideal class group of some
On the Growth ofp-Class Groups inp-Class Field Towers
โ Scribed by Farshid Hajir
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 166 KB
- Volume
- 188
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
โฆ Synopsis
Let p be a fixed prime number. By a p-extension of fields, we understand a Galois extension with pro-p Galois group. If k is a number field, let k ลฝฯฑ. be the maximal unramified p-extension of k s k ลฝ0. , and put ลฝ ลฝฯฑ. . ร ลฝ i. 4 ลฝ .
ลฝ 0 .
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