Coset of a Hypergroup (G,\circ_{N})
Article Sidebar
Main Article Content
Abstract
A hyperoperation on a nonempty set is a function
where
is the power set of
. The value of any
under
is denoted by
which is called the hyperproduct of
and
. If we have
is a group and
is a normal subgroup of
, then
is a hypergroup where the hyperoperationis
defined by
for all
.
We take a hyperoperation to construct cosets of any subgroup
of
instead of coset multiplication by binary operation of
and studies basic properties of this new structure of coset.
Downloads
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
References
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.