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

Let <f>F</f> be a finite field with <f>q</f> elements, and <f>T</f> a transcendental element over <f>F</f>. In this paper, we construct infinitely many real function fields of any fixed degree over <f>F(T)</f> 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 <f>m</f> and <f>n</f> with <f>m,n>1</f> and relatively prime to the characteristic of <f>F</f>, there are infinitely many imaginary fields of fixed degree <f>m</f> such that the class group contains a subgroup isomorphic to <f>(Z/nZ)m−1</f>. [Copyright &y& Elsevier]