Permutation Representations of the Orbits of the Automorphism Group of a   Finite Module over Discrete Valuation Ring
  Consider a discrete valuation ring $R$ whose residue field is finite of cardinality at least $3$. For a finite torsion module, we consider transitive subsets $O$ under the action of the automorphism group of the module. We prove that the associated permutation representation on the complex vector space $C[O]$ is multiplicity free. This is achieved by obtaining a complete description of the transitive subsets of $O\times O$ under the diagonal action of the automorphism group. 
C.P. Anil Kumar
math.RT math.CO math.RA