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Construction of ternary \(H_v\)-groups and ternary \(P\)-hyperoperations. (English) Zbl 1329.20080
Summary: In this paper, we study the concept of ternary \(H_v\)-groups and some of their properties. We give some examples of ternary \(H_v\)-groups. Also, we consider the fundamental relation \(\beta^*\) on a ternary \(H_v\)-group and prove that \(\beta^*\) is a compatible relation on a ternary \(H_v\)-group. In addition, we define the \(P\)-hyperoperation, and then, we construct a new ternary \(H_v\)-group.

MSC:
20N20 Hypergroups
20N15 \(n\)-ary systems \((n\ge 3)\)
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