On nilpotent and solvable pair of polygroups

Document Type : Original Article

Authors

1 Department of Mathematics, Faculty of Science, Payame Noor University, Tehran, Iran

2 Department of Mathematics, Faculty of Science, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran

Abstract

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 polygroups.

Keywords