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. 
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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