English

Free Bol loops of exponent two

Group Theory 2022-03-03 v1

Abstract

A Bol loop is a loop that satisfies the identity x((yz)y)=((xy)z)yx((yz)y)=((xy)z)y. In this paper, we give a construction of the free Bol loops of exponent two. We define a canonical form of all their elements and describe their multiplication law based on this form.

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Cite

@article{arxiv.2203.00808,
  title  = {Free Bol loops of exponent two},
  author = {Alexandre Grishkov and Marina Rasskazova and Giliard Souza dos Anjos},
  journal= {arXiv preprint arXiv:2203.00808},
  year   = {2022}
}

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16 pages