Abelian subgroups of any order in class groups of global function fields

AbstractLet F be a finite field with q elements, and T a transcendental element over F. In this paper, we construct infinitely many real function fields of any fixed degree over F(T) with ideal class numbers divisible by any given positive integer greater than 1. For imaginary function fields, we obtain a stronger result which shows that for any relatively prime integers m and n with m,n>1 and relatively prime to the characteristic of F, there are infinitely many imaginary fields of fixed degree m such that the class group contains a subgroup isomorphic to (Z/nZ)m−1