Geodesic
Structure of finitely generated commutative alternative algebras and special Moufang loops
Matematičeskie zametki, Tome 80 (2006) no. 3, pp. 413-420.

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It is proved that the commutator ideal of the multiplication algebra of a free commutative alternative algebra of rank $n$ is nilpotent of index $n-1$. As a corollary to this fact, the Bruck theorem for special commutative Moufang loops is derived.
Keywords: commutative Moufang loop, central nilpotency, alternative algebra, special Moufang loop. 
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S. V. Pchelintsev. Structure of finitely generated commutative alternative algebras and special Moufang loops. Matematičeskie zametki, Tome 80 (2006) no. 3, pp. 413-420. http://geodesic.mathdoc.fr/item/MZM_2006_80_3_a10/

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