Subgroups of Any Order in Class Groups of Global Function Fields
by
Allison M. Pacelli
Williams College

We will discuss function field analogues of previous results on the structure of the class group of an algebraic number field. In particular, given any positive integers m and n, relatively prime to the characteristic of F_q, there exist infinitely many function fields K of degree m over F_q(T) whose class group contains a subgroup isomorphic to (Z/nZ)^m-1 or Z/nZ depending on the behavior of the prime at infinity. In the special case that m is prime, we get a lower bound on the number of such fields.

Date received: October 2, 2003