Ideal class groups and subgroups of real quadratic function fields

In this paper we study the real quadratic function fields
$K = k (\sqrt{D})$
, given a necessary and sufficient condition for the ideal class group H K of any real quadratic function field K to have a cyclic subgroup of order n and obtained eight series of such fields. The ideal class numbers h(O
k
) of K in the series all have a factor n.