Quadratic function fields with invariant class group
β Scribed by Daniel J. Madden
- Publisher
- Elsevier Science
- Year
- 1977
- Tongue
- English
- Weight
- 503 KB
- Volume
- 9
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
For a prime number p, let β«ήβ¬ p be the finite field of cardinality p and X Ο X p a fixed indeterminate. We prove that for any natural number N, there exist infinitely many pairs ( p, K/β«ήβ¬ p (X )) of a prime number p and a ''real'' quadratic extension K/β«ήβ¬ p (X ) for which the genus of K is one and
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