Commutative Moufang loops and alternative algebras

@inproceedings{Grishkov2008CommutativeML,
  title={Commutative Moufang loops and alternative algebras},
  author={Alexander N. Grishkov and Ivan P. Shestakov},
  year={2008}
}
We compute the orders of free commutative Moufand loops of exponent 3 with n ≤ 7 free generators and find embeddings of such loops into a loop of invertible elements of the free commutative alternative algebra with identity x3 = 0.