Higher rank subgroups in the class groups of imaginary function fields

Let image be a finite field and T a transcendental element over image. In this paper, we construct, for integers m and n relatively prime to the characteristic of image, infinitely many imaginary function fields K of degree m over image whose class groups contain subgroups isomorphic to image. This increases the previous rank of m−1 found by the authors in [Y. Lee, A. Pacelli, Class groups of imaginary function fields: The inert case, Proc. Amer. Math. Soc. 133 (2005) 2883–2889].