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On the Class Group Problem for Function Fields

✍ Scribed by Bruno Angles

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 276 KB
Volume: 70
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1998.2225

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✦ Synopsis

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 number field. Furthermore, O. Yahagi [YAH] has proved that, if l is a prime number, every finite abelian l-group is isomorphic to the l-Sylow subgroup of the ideal class group of some number field. In this paper, we prove similar results for the function field case.

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