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Keywords:
Jordan loop; Jordan quasigroup; well-defined powers; nonassociative loop; order of a loop
Jordan loop; Jordan quasigroup; well-defined powers; nonassociative loop; order of a loop
Summary:
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 $9$.
References:
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