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arxiv: 1008.0700 · v1 · pith:ZD5HRLY6new · submitted 2010-08-04 · 🧮 math.GR

Powers of Elements in Jordan Loops

classification 🧮 math.GR
keywords jordanlooploopspowerscommutativeelementsestablishidentities
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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 $9$.

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