Higher rank subgroups in the class groups of imaginary function fields

Let FF be a finite field and TT a transcendental element over FF. In this paper, we construct, for integers mm and nn relatively prime to the characteristic of F(T)F(T), infinitely many imaginary function fields KK of degree mm over F(T)F(T) whose class groups contain subgroups isomorphic to (Z/nZ)m(Z/nZ)m. This increases the previous rank of m−1m−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].