English

The Moufang loops of order 64 and 81

Group Theory 2015-09-21 v1

Abstract

We classify Moufang loops of order 64 and 81 up to isomorphism, using a linear algebraic approach to central loop extensions. In addition to the 267 groups of order 64, there are 4262 nonassociative Moufang loops of order 64. In addition to the 1515 groups of order 8181, there are 55 nonassociative Moufang loops of order 8181, 22 of which are commutative.

Keywords

Cite

@article{arxiv.1509.05700,
  title  = {The Moufang loops of order 64 and 81},
  author = {Gábor P. Nagy and Petr Vojtěchovský},
  journal= {arXiv preprint arXiv:1509.05700},
  year   = {2015}
}