Fundamental Functor Based on Hypergroups and Groups

Document Type: Original Scientific Paper

Author

‎Department of Mathematics, ‎Payame Noor University‎, ‎Tehran‎, ‎I‎. ‎R‎. ‎Iran

Abstract

The purpose of this paper is to compute of fundamental relations
of hypergroups. In this regards first we study some basic properties of
fundamental relation of hypergroups, then we show that any given group is
isomorphic to the fundamental group of a nontrivial hypergroup. Finally we
study the connections between categories of hypergroups and groups via the
fundamental relatio

Keywords

Main Subjects


1. H‎. ‎Aghabozorgi‎, ‎B‎. ‎Davvaz and M‎. ‎Jafarpour‎, ‎Nilpotent groups derived from hypergroups‎, ‎J‎. ‎Algebra 382 (2013) 177-184‎.

2. P‎. ‎Corsini‎, ‎Prolegomena of Hypergroup theory‎, ‎Supplement to Riv‎. ‎Mat‎. ‎Pura Appl‎. ‎Aviani Editore‎, ‎Tricesimo‎, 1993‎.

3. P‎. ‎Corsini and V‎. ‎Leoreanu‎, ‎Applications of Hyperstructure Theory, ‎Advances in Mathematics (Dordrecht)‎, ‎5‎. ‎Kluwer Academic Publishers‎, ‎Dordrecht‎, ‎2003‎.

4. D‎. ‎Freni‎, ‎Une note sur le coeur d’un hypergroupe et sur la clôture transitive β de β‎, ‎(French) [A note on the core of a hypergroup and the transitive closure  β of β] Riv‎. ‎Mat‎. ‎Pura Appl. 8 (1991) 153-156‎.

5. D‎. ‎Freni‎, ‎A new characterization of the derived hypergroup via strongly regular equivalences‎, ‎Comm‎. Algebra 30(8) (2002) 3977-3989‎.

6. D‎. ‎Freni‎, ‎On a strongly regular relation in hypergroupoids‎, Pure Math‎. ‎Appl‎. ‎Ser‎. ‎A 3(3-4) (1992) 191-198‎.

7. D‎. ‎Freni‎, ‎Hypergroupoids and fundamental relations‎, ‎In‎: ‎Proceedings of the 5th International Congress on Algebraic Hyperstructures and Applications (Iasi 1993)‎,M‎. ‎Stefanescu(ed.)‎, ‎Hadronic Press‎, ‎Palm Harbor‎, ‎FL‎, USA‎, ‎(1994) pp‎. ‎81-92‎.

 

8. M‎. ‎Hamidi‎, ‎A‎. ‎Borumand Saeid and V‎. ‎Leoreanu-Fotea‎, ‎Divisible groups derived from divisible hypergroups‎, Politehn‎. ‎Univ‎. ‎Bucharest Sci‎. ‎Bull‎. ‎Ser‎. ‎A Appl‎. ‎Math‎. ‎Phys. 79(2) (2017) 59-70‎.

 

9. M‎. ‎Koskas‎, ‎Groupoides‎, ‎demi-hypergroupes et hypergroupes (French)‎, ‎J‎. ‎Math‎. ‎Pures Appl‎. ‎(9) 49 (1970) 155-192‎.

 

10. F‎. ‎Marty‎, ‎Sur une generalization de la notion de groupe‎, ‎In‎: ‎Proceedings of 8th Congres Math‎. Scandinaves‎, ‎Stockholm (1934) pp‎. ‎45-49‎.

 

11. S‎. ‎Sh‎. ‎Mousavi and M‎. ‎Jafarpour‎, ‎On free and weak free (semi)hypergroups‎, Algebra Colloq. 18(1) (2011) 873-880‎.

 

12. T‎. ‎Vougiouklis‎, ‎Hyperstructures and Their Representations‎, ‎Hadronic Press Monographs in Mathematics‎, ‎Hadronic Press‎, ‎Inc.‎, ‎Palm Harbor‎, ‎FL‎, ‎1994‎.