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Exponentiation and the identity \(x^ 2y=(xy)^ 2\). (English) Zbl 0556.20053
Let G be a groupoid. Put \(x^{n+1}=x^ nx\) for every \(x\in G\) and all positive integers n. Further, let S(x) denote the subgroupoid generated by x and \(P(x)=\{x^ n\); \(n\in N\}\). In the paper, some relations between S(x) and P(x) are established for right bi-distributive groupoids (a groupoid is said to be right bi-distributive if it satisfies the identity \(x^ 2y=xy\cdot xy)\).
Reviewer: T.Kepka

MSC:
20N99 Other generalizations of groups
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