Links Between HX-Groups and Hypergroups  

作　　者：Irina Cristea Michal Novák Babatunde Oluwaseun Onasanya 

机构地区：[1]Centre for Information Technologies and Applied Mathematics University of Nova Gorica,Slovenia [2]Faculty of Electrical Engineering and Communication Brno University of Technology,Czech Republic [3]Key Laboratory of Intelligent Information Processing and Control of Chongqing Municipal Institutions of Higher Education Chongqing Three Gorges University,Chongqing 404000,China [4]Department of Mathematics,University of Ibadan,Nigeria

出　　处：《Algebra Colloquium》2021年第3期441-452,共12页代数集刊（英文版）

基　　金：The first author acknowledges the financial support from the Slovenian Research Agency(research core funding No.P1-0285);The second author was supported by the FEKT-S-17-4225 grant of Brno University of Technology.

摘　　要：The concept of an HX-group is an upgrade of the concept of a group,in which a new operation is defined on the family of non-empty subsets of a group.If this new support set together with the new operation is a group,then we call it an HX-group.On the other hand,a hyperoperation is a mapping having the same codomain as the operation of an HX-group,i.e.,the family of non-empty subsets of the initial set,but a different domain-the set itself.This could be(and was indeed)a source of confusion,which is clarified in this paper.Moreover,HX-groups naturally lead to constructions of hypergroups.The links between these two algebraic concepts are presented,with the aim of reviving the old notion of an HX-group in the current research on algebraic hyperstructures.One of such existing links and one newly established link are also discussed.

关 键 词：HX-group hyperstructure theory Chinese hypergroupoid EL-hyperstructure power set 

分 类 号：O15[理学—数学]