The Number of Homomorphisms from a Finite Abelian Group to a Symmetric Group (II)

For any finite abelian group A, we give the lower bound of ordp(|Hom(A, Sn)|), and determine the region of convergence of the p-adic power series 1 + Sigma(infinity)(n=1) vertical bar Hom(A, S-n)vertical bar X-n/ n!.2000 Mathematics Subject Classication: Primary 05A15; Secondary 20B30; 20K01; 20K2