  We summarize recent work on the classification of modular invariant partition
functions that can be obtained with simple currents in theories with a center
(Z_p)^k with p prime. New empirical results for other centers are also
presented. Our observation that the total number of invariants is
monodromy-independent for (Z_p)^k appears to be true in general as well. (Talk
presented in the parallel session on string theory of the Lepton-Photon/EPS
Conference, Geneva, 1991.)
