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2021•Journal of algebraic hyperstructures and logical algebrasOpen access

On nilpotent and solvable pair of polygroups

E. Mohammadzadeh, Fahimeh Mohammadzadeh

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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.

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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.

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Available 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.

Key concepts: Nilpotent, Nilpotent group, Mathematics, Pure mathematics, Combinatorics, Solvable group, Discrete mathematics, Abelian group

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