On subgroup perfect codes in Cayley graphs

A perfect code in a graph ?=(V,E) is subset C of V such that no two vertices are adjacent and every vertex V?C to exactly one C. subgroup H group G called if there exists Cayley which admits as code. Equivalently, an inverse-closed containing the identity element (A,H) tiling sense can be uniquely expressed product H. In this paper we obtain multiple results on codes finite groups, including few necessary sufficient conditions for code, involving 2-subgroups study codes, several metabelian generalized dihedral nilpotent groups 2-groups.