On the Class Group Problem for Function Fields Original Research Article

LetGbe a finite abelian group, it is a difficult and unsolved problem to find a number fieldFwhose ideal class group is isomorphic toG. 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.