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

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Witthawas Phanthawimol


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

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


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How to Cite
Phanthawimol, W. (2022). Coset of a Hypergroup (G,\circ_{N}). Journal of Science Ladkrabang, 31(2), 130–139. Retrieved from
Research article


Pinter, C. C. 1971. Set Theory, Additon – Wesley, Massaehuselts.

มานัส บุญยัง. 2556. พีชคณิตนามธรรม 1. พิมพ์ครั้งที่ 5, สำนักพิมพ์มหาวิทยาลัยรามคำแหง, กรุงเทพมหานคร. [Manus Boonyang. 2013. Abstract Algebra . 5thed, Ramkhamhaeng University Press, Bangkok. (in Thai)]

Fraleigh, John B. 1980. A First Course in Abstract Algebra, Addison-Wesley, Reading Massachusettes.

Birkhoff, G. and Bartee, Thomas C. 1970. Modern Applied Algebra, McGraw-Hill Book Company, New York.

Corsini, P. 1993. Prolegomenu of Hypergroup Theory, AvianiEditove, Udine Ltaly.