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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
##### Keywords:
subgroupoid; right bi-distributive groupoids
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