On nilpotent and solvable pair of polygroups

In this paper, we introduce nilpotent and solvable pair of polygroups. By a pair of polygroups (P, N), we mean a polygroup P with a normal sub-polygroup N of P . In addition, we obtain a necessary and sufficient condition between nilpotency (solvability) of pair of polygroups and pair of groups. In particular, we extend the theory of groups to a pair of polygroups. Finally, we study the relationship between nilpotent and solvable pair of poly-groups.