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Derived metabelian groups from hv-groups | ||
| Journal of Hyperstructures | ||
| دوره 8، شماره 1، شهریور 2019، صفحه 58-68 اصل مقاله (339.5 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2019.2613 | ||
| نویسندگان | ||
| Morteza Jafarpour* ؛ Mahdiyeh Iranmanesh؛ Hossien Aghabozorgi | ||
| Department of Mathematics, Vali-e-Asr university of Rafsanjan, Iran | ||
| چکیده | ||
| In this paper first we introduce and analyze a new definition of left and right commutators in Hv-group. Secondly, using commutators we introduce a new strongly equivalence relation π∗ on an Hv-group H such that the quotient H/π∗, the set of all equivalence classes, is a metabelian group. Then we introduce metabelian Hv-groups and investigate some of their properties. Finally, we investigate some properties of commutators for the class of weak polygroups. | ||
| کلیدواژه‌ها | ||
| Hv-group؛ metabelian group؛ metabelian Hv-group؛ weak polygroup | ||
| مراجع | ||
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[1] H. Aghabozorgi, B. Davvaz, M. Jafarpour, Solvable polygroups and derived sub-polygroups, Comm. Algebra, 41 (2013), 3098-3107. [2] P. Corsini, Prolegomena of Hypergroup Theory, Aviani Editore, Tricesimo, 1993. [3] P. Corsini and V. Leoreanu, Applications of Hyperstructure Theory, Kluwer Aca-demical Publications, Dordrecht, 2003. [4] P. Corsini and V. Leoreanu, About the heart of a hypergroup, Acta Univ. Caroli-nae, 37 (1996) 17-28. [5] B. Davvaz, Polygroup Theory and Related Systems, World Scientific, 2013. [6] B., Davvaz, T., Vougiouklis, Commutative rings obtained from hyperrings (Hv-rings) with α∗ -relations, Comm. Algebra, 2007, 35:11, 3307-3320. [7] D. Freni, A new characterization of the derived hypergroup via strongly regular equivalences, Comm. Algebra, 2002, 30:8, 3977-3989. [8] M. Koskas, Groupoids, demi-hypergroupes et hypergroupes, J. Math. Pure Appl.,1970, 49:9, 155-192. [9] F.Marty,Sur une Generalization de la Notion de Groupe,8th Congress Math.Scandenaves,Stockholm,Sweden,(1934)45-49. [10] M. Norouzi, I. Cristea, Fundamental relation on m-idempotent hyperrings. Open Math. 2017; 15: 15581567. [11] T. Vougiouklis, Hyperstructures and Their Representations, Hadronic Press,Palm Harbor, FL, 1994. [12] T. Vougiouklis. The fundamental relation in hyperrings, The general hyperfield, Proc. 4th Internat. Congr. AHA, Xanthi, 1990 (World Scientific, Singapore,1991) 209-217. [13] T. Vougiouklis, Groups in hypergroups, Combinatorics ’86 (Trento, 1986), 459–467, Ann. Discrete Math., 37, North-Holland, Amsterdam, 1988. [14] T. Vougiouklis, The fundamental relation in hyperrings. The general hyperfield, Algebraic hyperstructures and applications (Xanthi, 1990), World Sci. Publ.,Teaneck, NJ, 1991, 203-211. | ||
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