# Coset of a Hypergroup (G,\circ_{N})

## Abstract

A hyperoperation on a nonempty set $H$ is a function $\circ&space;:&space;H\times&space;H\rightarrow&space;P(H)\setminus&space;\{&space;\varnothing&space;\}$ where $P(H)$ is the power set of $H$. The value of any $(x,y)\in&space;H\times&space;H$ under $\circ$ is denoted by $x\circ&space;y$ which is called the hyperproduct of $x$ and $y$. If we have $G$ is a group and $N$ is a normal subgroup of $G$, then $(G,\circ&space;_{N})$ is a hypergroup where the hyperoperationis $\circ&space;_{N}$ defined by $x\circ_{N}y=(xy)N$ for all $x,y\in&space;G$.

We take a hyperoperation $\circ&space;_{N}$ to construct cosets of any subgroup $H$ of $G$ instead of coset multiplication by binary operation of $G$ and studies basic properties of this new structure of coset.

## Article Details

How to Cite
Phanthawimol, W. (2022). Coset of a Hypergroup (G,\circ_{N}). Journal of Science Ladkrabang, 31(2), 130–139. Retrieved from https://li01.tci-thaijo.org/index.php/science_kmitl/article/view/252826
Section
Research article

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