Lagrange Theorem for polygroups

Abstract

So far, isomorphism theorems in hyperstructure were proved for different structures of polygroups, hyperrings and etc. Inthis paper, the polygroups properties is studied with the introduction of a suitable equivalence relation. We show that the above relationis strongly regular. Our main purpose in the paper is investigating Lagrang theorem and other expressing of isomorphism theorems forpolygroups

Keywords

• polygroup,Lagrange theorem,isomorphism theorems,fundamental relation,heart of hypergroup

References

1. Asghari-Larimi M, Corsini P, Ranjbar-Yanehsari E. 2012. Intuitionistic fuzzy sets and join spaces associated with nary membership functions, The Journal of Mathematics and Computer Science, Vol .5 No.2, 115-125.
2. Asghari-Larimi M, Davvaz B. 2010. Hyperstructures associated to arithmetic functions, ArsCombitoria, vol.97 , 51-63.
3. Asghari-Larimi M, Leoreanu-Fotea V. 2009. A connection between hypergroupoids and L-FuzzySets of Type 2, Italian J. of Pure and Appl. Math., vol.26, 207-216.
4. Corsini P. 1993. Join spaces, power sets, fuzzy sets, Algebraic hyperstructures and applications, Hadronic .
5. Corsini P. 1993. Prolegomena of Hypergroup Theory, second eddition, Aviani.
6. Davvaz B. 2010. Isomorphism theorems of polygroups. Bull. Malays. Math. Sci. Soc. (2) 33, No. 3, 385-392. ISSN 0126-6705.
7. Davvaz B, Leoreanu-Fotea V. 2007. Hyperring Theory and Applications, International Academic Press, USA, 347.
8. Jantociak J. 1991. Homomorphisms, equivalences and reductions in hypergroups, Rivista di Mat. Pure ed Appl. 9, 2B.

9. Marty F. 1934, Sur une gnralisation de la notion de group, in: 4th Congress Math. Scandinaves, Stockholm, pp. 45-49.ress, Palm Harbor, 45-52.
10. Ranjbar-Yanehsari E, Asghari-Larimi M. 2011. Some Properties of Hyperstructure and Union Normal Fuzzy Subgroups, International Mathematical Forum Vol. 6, no. 53, 2645 2653.
11. Zahedi. M, Bolurian. M, Hasankhani. A. 1995. On polygroups and fuzzy sub- polygroups, J. Fuzzy Math. 1, 115.