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arxiv: 0811.3787 · v1 · submitted 2008-11-24 · 🧮 math.RA · math.CO

Commutative Moufang loops and alternative algebras

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keywords commutativefreeloopsalternativealgebraalgebrascomputeelements
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We compute the orders of free commutative Moufand loops of exponent 3 with $n\leq 7$ free generators and find embeddings of such loops into a loop of invertible elements of the free commutative alternative algebra with identity $x^3=0$.

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