Geodesic
Powers of elements in Jordan loops
Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 2, pp. 291-299.

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A Jordan loop is a commutative loop satisfying the Jordan identity $(x^2 y)x = x^2(y x)$. We establish several identities involving powers in Jordan loops and show that there is no nonassociative Jordan loop of order $9$.
Classification : 20N05
Keywords: Jordan loop; Jordan quasigroup; well-defined powers; nonassociative loop; order of a loop 
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     author = {Pula, Kyle},
     title = {Powers of elements in {Jordan} loops},
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     pages = {291--299},
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     zbl = {1192.20060},
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     url = {http://geodesic.mathdoc.fr/item/CMUC_2008__49_2_a10/}
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Pula, Kyle. Powers of elements in Jordan loops. Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 2, pp. 291-299. http://geodesic.mathdoc.fr/item/CMUC_2008__49_2_a10/