Asymptotics of abelian group-partitions and associated Dirichlet series
  We introduce a notion of a group-partition for a finite Abelian group, which is a generalized notion of the standard partition. To obtain asymptoticdistributions of group-partition, we study the Dirichlet series for group-partitions by employing the generating function of the plane partition. 
Tetsuya Momotani