【摘 要】
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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 othe
【机 构】
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Centre for Information Technologies and Applied Mathematics University of Nova Gorica,Slovenia;Facul
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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.
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